Prove that () = + 5 and () = √ − 5 are inverse functions without finding the inverse of either function.
Answers
if two functions are inverse of each other, that means that their composite will result in "x" alone.
meaning, that if f(x) and g(x) are inverse of each other, then f( g(x) ) = x and the other way around will be the same, hmmm let's see if that's true
[tex]f(x)=x^3 + 5\hspace{5em}g(x)=\sqrt[3]{x-5} \\\\[-0.35em] ~\dotfill\\\\ f( ~~ g(x) ~~ )=[g(x)]^3 + 5\implies f( ~~ g(x) ~~ )=[\sqrt[3]{x-5}]^3 + 5 \\\\\\ f( ~~ g(x) ~~ )=(x-5) + 5\implies f( ~~ g(x) ~~ )=x ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ g( ~~ f(x) ~~ )=\sqrt[3]{[f(x)]-5}\implies g( ~~ f(x) ~~ )=\sqrt[3]{[x^3 + 5]-5} \\\\\\ g( ~~ f(x) ~~ )=\sqrt[3]{x^3}\implies g( ~~ f(x) ~~ )=x ~~ \textit{\LARGE \checkmark}[/tex]
Related Questions
When you apply the method to complete the square to find the solution to the equation
2x^2 +3x +3=4
What term should we sum/add on both sides of the equation?
A. 9
B. 9/4
C. 3/2
D. 9/16
Answers
Answer:
B
Step-by-step explanation:
x² + 3x + 3 = 4 ( subtract 3 from both sides )
x² + 3x = 1
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2( [tex]\frac{3}{2}[/tex] )x + ([tex]\frac{3}{2}[/tex] )² = 1 + ( [tex]\frac{3}{2}[/tex] )²
(x + [tex]\frac{3}{2}[/tex] )² + [tex]\frac{9}{4}[/tex] = 1 + [tex]\frac{9}{4}[/tex]
that is [tex]\frac{9}{4}[/tex] is added to both sides
And adult plate costs $8
A child plate costs $5
Total plates sold is 272
Total value is $1,933
How many of each plate were sold?
Answers
191 of adult plates and 81 child plates were sold.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Adult plate costs A= $8
Child plate costs C=$5
Total plates sold is 272
A+C=272..(1)
8A+5C=1,933..(2)
C=272-A
Substitute in equation 2
8A+5(272-A)=1933
8A+1360-5A=1933
1360+3A=1933
Subtract 1360 on both sides
3A=1933-1360
3A=573
Divide both sides by 3
A=191
Now substitute A value in 1
191+C=272
Subtract 191 on both sides
C=272-191
C=81
Hence, 191 of adult plates and 81 child plates were sold.
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If Malik has 4 times as many nickels as quarters and they have a combined value of 315 cents, how many of each coin does he have?
Answers
Set up your equation
4q + q = 315 Add (q = amount of quarters)
5q = 315 Divide
q = 63
Therefore he has 63 quarters.
To find the amount of nickels, multiply 4 and 63
4 x 63 = 252
Therefore he has 63 quarters and 252 nickels.
I hope this helps! :)
Find the values of x and y.
x + 2 = 3y
Answers
The number of solution of the equation x + 2 = 3y will be infinite for the infinite value of 'x'. The solution is (1, 1).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given below.
x + 2 = 3y
There is only one equation, so we have to assume 'x'.
If x = 1, then the value of the variable 'y' is given as,
3y = 1 + 2
3y = 3
y = 3 / 3
y = 1
Similarly, the number of solution of the equation x + 2 = 3y will be infinite for the infinite value of 'x'.
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If the change in velocity of a car is 30 m/s and the time interval is 5 seconds, the acceleration of the car is ________ m/s2
Answers
The acceleration of the car is 6m/s²
What is acceleration?Acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities. Acceleration is measured in meter per second squared
It can also be defined as the ratio of the change in velocity to the time
Therefore acceleration is given as (v-u)/t
where v is the final velocity and u is the initial velocity, t is the time
therefore a= 30-0/5
a= 30/5
a= 6m/s²
therefore the acceleration of the car is 6m/s²
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Evaluate 25 - 4x when x = 2 and when x = 3. Which gives you the larger value and
what is that value?
O x = 2 will give you the larger value of 17.
O x = 3 will give you the larger value of 63.
O x = 2 will give you the larger value of 42.
O x = 3 will give you the larger value of 13.
Answers
Answer:17
Step-by-step explanation:
Substitute: 25-4x2
Calculate the product or quotient: 25-8
Calculate the sum or difference: 17
Answer: 17
Select all the equations that represent a line passing through the point (5,-2) with a slope of 4.
Answers
Answer:
y = 4x - 22
Step-by-step explanation:
y = 4x + b
-2 = 4(5) + b
-2 = 20 + b
b = -22
y = 4x - 22
When Max moved to a
new school in 6th
grade, there were
only 3 other kids he
knew at the entire
school. There were
367 kids in the school.
What percentage of
kids did Max know?
Answers
the answer is =0.82%
Evaluate the expression 9x - 5 for the values of x given in the first column.
Value of x Value of expression
5
4
129
6
7
Answers
Answer:
Step-by-step explanation:
To fill the table using the expression
you have to replace each value with x and solve the expression
Answer:
Step-by-step explanation:
Expression : 9x - 5
To fill the table using the expression, you have to replace each value with x and solve the expression.
The answer is attached to the picture.
what is the equation for a line that passes through (3.4) and 4,9
Answers
The equation of the line in slope-intercept form that passes through (3, 4) and (4, 9) is: y = 5x - 11.
How to Find the Equation of a Line?The equation of a line can be written in point-slope form as y - b = m(x - a), if we know the slope (m) and a point (a, b) on the line. It can be rewritten to the slope-intercept form as y = mx + b.
Given the points on a line:
(3, 4) and (4, 9)
Slope of the line (m) = change in y / change in x = (9 - 4)/(4 - 3)
Slope of the line (m) = 5/1
m = 5
To write the equation of the line, substitute m = 5 and (a, b) = (3, 4) into y - b = m(x - a):
y - 4 = 5(x - 3)
Rewrite in slope-intercept form:
y - 4 = 5x - 15
y = 5x - 15 + 4
y = 5x - 11 [equation of the line]
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Which set of ordered pairs (x, y) could represent a linear function?
A = {(-6,9), (-3,6), (0,3), (4,0)}
B = {(1, 1), (2,3), (4,5), (5,7)}
C = {(-4,-4), (-2,-2), (1,0), (4,3)}
D = {(3,7), (5, 1), (6,-2), (7,-5)}
Answers
What is 31+4 × [11-(1+3)] =
Answers
Answer:
59
Step-by-step explanation:
31+4 × [11-(1+3)]
31+4*[11-4]
31+4*(7)
31+28
59
The easy Answer is 59. When doing these types of questions remember:
Parentheses
Exponents
Multiplication
Divionsion
Add
Subtract
Isaiah is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from his sales that day. The equation P=0.025x+85P=0.025x+85 represents Isaiah's total pay on a day on which he sells xx dollars worth of computers. What is the yy-intercept of the equation and what is its interpretation in the context of the problem?
Answers
Answer:
$85
Step-by-step explanation:
x=0 p= 85 => (0,85) {y-intercept}
p=0 x= -3400 => (-3400,0) {x-intercept}
y-intercept means Isaiah sells $0, then the company will pay him $85.
Lisa received 20% discount on a video game she bought. The discount was $5. What is the
regular price of the video game?
Answers
A new corporation has established itself and is set to start selling shares of stock. On the first day, you purchase 100 shares of stock at $23.00 per share. Three years later, you sell the stock for $45.00 per share.
a. How much did you net from the sale?
b. Was this a capital gain or a capital loss?
Answers
a) The net for the sale is: $4,500
b) The capital gain is $2,200
How much did you net from the sale?
We know that you had 100 shares, now the value of each of these is $45.00, then the amount that you make if you sell the 100 shares is:
S = 100*$45.00 = $4,500
How to get the capital gain?The capital gain is the difference between the amount we found above and the amount you paid for the shares.
The price of the shares was $23.00, then the amount you paid is:
C = $23.00*100 = $2,300
Then the capital gain is:
g = $4,500 - $2,300 = $2,200
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p. Determine which of the values in the set {-5, -1, 0, 3}, if any, make the equation 4 = m +5 - 2m true.
Answers
Answer:
None of the values.
Step-by-step explanation:
Simplify the given equation.
First, simplify by combining like terms. Like terms are terms that share the same amount of the same variables:
4 = m + 5 - 2m
4 = (m - 2m) + 5
4 = -m + 5
Next, isolate the variable, m. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
-
First, subtract 5 from both sides of the equation:
4 = -m + 5
4 (-5) = -m + 5 (-5)
4 - 5 = -m
-1 = -m
Next, isolate the variable m. Remove the negative sign by dividing -1 from both sides of the equation:
(-1)/-1 = (-m)/-1
m = -1/-1 = 1
None of the values will make the equation true, as 1 is not a given value.
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Which expression represents "10 subtracted from the quotient of 3 and a number"?
Answers
Answer:
Step-by-step explanation:
[tex]\frac{3}{n}[/tex] - 10.
The quotient of 3 and a number translates to [tex]\frac{3}{n}[/tex], then, all you have to do is subtract 10 from that value, giving the expression above.
Carson measured a line to be 2.2 inches long. If the actual length of the line is 2.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answers
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percentage error of the measurement is 47.8%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The actual length of the line = 2.3 inches
The measured length of the line = 2.2 inches
The error length of the line.
= 2.3 - 2.2
= 1.1 inches
The percentage error of the measurement.
= 1.1/2.3 x 100
= 47.8%
Thus,
The percentage error of the measurement is 47.8%.
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what is the volume of the composite figure 16 7 3 5 3 6
Answers
The total volume of the composite figure is; 381 m³
How to find the volume of the composite figure?The formula for volume of a prism is;
V = Bh
where;
B is area of triangular base
h is height of prism
Thus;
V = (¹/₂ * 3 * 5) * 6
V = 45 m³
Volume of bottom cuboid is given by the formula;
V = Length * width * height
Thus;
V = 16 * 7 * 3
V = 336 m³
Total volume of composite figure = 45 m³ + 336 m³
Total volume of composite figure = 381 m³
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can anyone help me? I don't know the answer.
Answers
Answer: 27/70
the area of the shaded rectangle
Step-by-step explanation:
9/10 and 3/7 of the rectangle are shaded on top and bttom. So you multiple this together and you will get 27/70
9/10 x 3/7 = 27/70
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What is the sum of the series sum from n equals 1 to infinity of negative 3 times three eighths to the n power question mark
Answers
The required sum of the series sum from n equals 1 to infinity is -9/5
What is geometric series of infinity?geometric series, in science, a infinite series of the structure a + ar + ar^2 + ar^3+⋯, where r is known as the common ratio. A basic model is the mathematical series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +⋯, which joins to an amount of 2 (or 1 on the off chance that the initial term is barred).
According to question:We have,
GP; -3(3/8), -3(3/8)^2,................ -3(3/8)^∞
Common ratio(r) = 3/8, a = -9/8
S(1 to ∞) = a/(1 - r)
S(1 to ∞) = -9/8(1 - 3/8)
S(1 to ∞) = -9/8/5/8
S(1 to ∞) = -9/5
Thus, sum of geometric series is -9/5.
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Dan reads his favorite series of books at a rate of 19
pages per hour. If Dan has already read the series for
34 hours but still has 1193 pages left, how many pages
are in the series altogether?
Answers
Answer:
Step-by-step explanation:
mult 19 buy 34 to find total number of page read then add page left = 1839
PQTU and PRSU are rectangles.
PU = 11 cm
PQ = 4 cm
QR = 3 cm
Work out
perimeter PQTU: perimeter PRSU
Give your answer in its simplest form
Answers
The value of the ratio of the perimeters of the rectangles PQTU and PRSU is 30:36, that is 5:6.
Define Perimeter.The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Equation for perimeter of a rectangle (P) =2 (l + w), where l is the length and w is the width.
In the question, length of rectangle PQTU= 11cm
Width of rectangle PQTU= 4 cm
Perimeter of rectangle PQTU= 2( 11+4)
= 2 x 15
= 30 cm
The length of the rectangle PRSU= 11cm
The width of the rectangle PRSU= PQ + QR
= 4+3 = 7
The perimeter of the rectangle PRSU= 2(11+7)
= 36 cm
Therefore, perimeter of PQTU: perimeter of PRSU = 30:36
Dividing by 6 on both= 30/6 :36/6 = 5:6
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If the point D (-6, 9) is reflected over the x-axis, the coordinates of D’ would be?
Answers
Answer:
D'(-6, -9)
Step-by-step explanation:
When a point is reflected over the x-axis, the x-coordinate remains the same. The reflected point is the same distance from the x-axis as the original point, but it's on the other side of the x-axis, so the y-coordinate changes sign.
In general, point (x, y) reflected over the x-axis becomes point (x, -y).
Here, point D(-6, 9) becomes point D'(-6, -9).
The graph of x=6(y+6)^2+1 is a parabola with vertex (−6,1) and opening to the right.
answer options:
Answers
By the definition of the vertex form of the quadratic equation x - 1 = 6 · (y + 6)² has its vertex at (h, k) = (- 6, 1) and opens to the right. (Correct choices: A, B)
How to determine the features of a quadratic equation
In this problem we find the definition of a quadratic equation in vertex form, whose axis of symmetry is parallel to the x-axis. This form of quadratic equation is described below:
x - h = C · (y - k)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.
Please notice that the parabola opens to the right (+ x direction) when the vertex constant is greater than 0. By direct inspection, we have the following conclusions:
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Write an equation in slope-intercept form of the line given:
Answers
Answer: y=-x
Step-by-step explanation:
Choose 2 coordinates: (-2,2) and (2,-2)
Let us find the slope m:
[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=-2\ \ \ \ \ x_2=2\ \ \ \ \ y_1=2\ \ \ \ \ y_2=-2\\\\m=\frac{-2-2}{2-(-2)} \\\\m=\frac{-4}{2+2} \\\\m=\frac{-4}{4} \\\\m=-1\\[/tex]
Hence,
y=-x+b
To find the coefficient b, choose any coordinate belonging to the given line, for example (-2,2):
2=-(-2)+b
2=2+b
0=b
Hence, b=0
Thus, y=-x
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What is the sum of the infinite geometric series?
25 minus 10 plus 4 minus eight fifths plus continuing
The series diverges.
five halves
fifty sevenths
one hundred twenty-five sevenths
eighty-seven fifths
Answers
Answer: [tex]C. \frac{125}{7}[/tex]
Step-by-step explanation:
1. Find the sum of the infinite geometric sequence:
[tex]S = \frac{125}{7}[/tex]
2. Find the correct option:
C
What is the solution of this inequality?
r−6>−11
Drag and drop the choices to correctly complete the inequality.
help
Answers
The solution to the given linear inequality, r - 6 > -11, is r > -5
Solving Linear InequalitiesFrom the question, we are to determine the solution of the given inequality
The given inequality is
r - 6 > -11
To determine the solution of the inequality, we will solve the inequality for the unknown variable.
In the inequality, the unknown variable is r.
Solving the inequality for r
r - 6 > -11
Add 6 to both sides
r - 6 + 6 > -11 + 6
r > -5
Hence, the solution is r > -5
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Using the simplex tableau solve for the LPP.
Objective function z=x1+2x2
Constraints
2x1 + x2<8
X1 + x2 <5
X1,x2>0
Answers
The values of the objective function obtained for the given set of equation is 7.
Define the term LPP?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.For the stated question-
Objective function z = x1+2x2
Constraints
2x1 + x2<8 ....eq 1x1 + x2 <5 ....eq 2x1, x2>0 .....eq 3Subtract equation 2 from 1.
x1 = 8 - 5
x1 = 3
Put value if x1 in eq 2
x1 + x2 = 5
x2 = 5 - 3
x2 = 2
Put the values of x1 and x2 in Objective function
z = x1 + 2x2
z = 3 + 2x2
z = 7
Thus, the values of the objective function obtained for the given set of equation is 7.
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A 9-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
(Pls help)
Answers
Answer: 0.75 inches per hour
Step-by-step explanation:
9/12=0.75
0.75 x 12 = 9
0.75 inches per hour
Answer: 4.5 hours.
Step-by-step explanation:
Use a proportion.
3 3/8 = 3.375
9 inch is to 12 hours as 3.75 inches is to x hours.
9/12 = 3.375/x
3/4 = 3.375/x
3x = 4 * 3.375
x = 4 * 1.125
x = 4.5
Answer: 4.5 hours