Select the correct answer from each drop-down menu.
Consider these functions:
For x ≥ 0, the value of f(g(x)) is __
For x ≥ 0, the value of g(f(x)) is __
For x ≥ 0, functions f and g __ inverse functions.
Choices:
1. x,4x,8x
2. x,4x,8x
3. are, are not
Answers
Answer:
x
x
are
Step-by-step explanation:
For x ≥ 0, the value of f(g(x)) is x,For x ≥ 0, the value of g(f(x)) will be x and functions f and g are inverse functions.Option a from all the choices is corect.
What is a function?A connection between independent variables and the dependent variable.is defined by the function.
Functions help to represent graphs and equations. A function is represented by two variables one is dependent and another one is an independent function.
The relation between them is shown as y if dependent and x is the independent variable;
Given function;
f(x) = 16x²
g(x)=(1/4)√x
For x ≥ 0, the value of f(g(x)) is found as;
f(x) = 16x²
[tex]\rm f(g(x)) = 16 (\frac{1}{4} \sqrt x) ^2\\\\ f(g(x)) =\frac{16}{16} x\\\\ f(g(x)) = x[/tex]
For x ≥ 0, the value of g(f(x)) is
g(x)=(1/4)√x
[tex]\rm g(x)=\frac{1}{4}\sqrt x \\\\ g(x ) = \frac{1}{4} \times \sqrt{16 \ x^2}\\\\ g(x) = \frac{4}{4} x \\\\ g(x) = x[/tex]
For x ≥ 0, functions f and g are inverse functions
Let,
y=F(X)
If,
y= 16x²
x=16y²
y² = x/16
y=(1/4)√x
Hence,For x ≥ 0, the value of f(g(x)),For x ≥ 0, the value of g(f(x)) will be x and x respectively.and For x ≥ 0, functions f and g are inverse functions.
Hence, option a from all the choices is corect.
To learn more about the function refer to the link https://brainly.com/question/12431044.
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Related Questions
PLZ Help Urgent. 15 POINTS, BRAINLY Guaranteed.
Plz Answer honestly or you will be reported.
Multiply.
15 ⋅ 1/3
1/45
1/5
5
45
Answers
Answer:
5
Step-by-step explanation:
[tex]\frac{15}{1}[/tex] multiplied by [tex]\frac{1}{3}[/tex]
which makes: [tex]\frac{15}{3}[/tex]
simplify: 5
Two cards are drawn in succession from a standard 52-card deck.1. What is the probability that the first card is red and the second card is black(A) If the cards are drawn without replacement?(B) If the cards are drawn with replacement?2. Two balls are drawn in succession out of a box containing 3 red and 5 white balls. Find the probability that at least 1 ball was red, given that the first ball was(A) Replaced before the second draw(B) Not replaced before the second drawContext Header: Conditional ProbabilityContext Section:Conditional Probability is a calculation of the likelihood of an occurrence provided that another event has already occurred. Conditional probability A provided B is generally written as:P(A/B)=P(A∩B)P(B)
Answers
Answer:
52 cards:
26 red and 26 black
P(R) = probability of picking a red card
P(B) = probability of picking a black card
P(R) = P(B) = ¹/₂
If with replacement:
P(R∩B) = (¹/₂)(¹/₂) = ¹/₄
If without replacement:
P(R∩B) = (¹/₂)(²⁶/₅₁) = ¹³/₅₁
8 Balls:
3 red and 5 white
P(R) = probability of picking a red ball
P(W) = probability of picking a white ball
P(R) = ³/₈
P(W) = ⁵/₈
If with replacement:
P(R∩W) ∪ P(W∩R) = (³/₈)(⁵/₈) + (⁵/₈)(³/₈)
= ¹⁵/₆₄ + ¹⁵/₆₄
= ³⁰/₆₄
= ¹⁵/₃₂
If without replacement:
P(R∩W) ∪ P(W∩R) = (³/₈)(⁵/₇) + (⁵/₈)(³/₇)
= ¹⁵/₄₂ + ¹⁵/₄₂
= ³⁰/₄₂
= ⁵/₇
Solve the system of equations algebraically.
5x - 3y = 6
6x - 4y = 2
a. many solutions
C.
no solution
b. (8, 14
d. (9. 13)
Please select the best answer from the choices provided
Ο Α
ОВ
О С
Answers
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=9,\:y=13[/tex]
the option 'd' is correct.
Step-by-step explanation:
Given the system of the equations
[tex]\begin{bmatrix}5x-3y=6\\ 6x-4y=2\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}5x-3y=6\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:30x-18y=36[/tex]
[tex]\mathrm{Multiply\:}6x-4y=2\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:30x-20y=10[/tex]
[tex]\begin{bmatrix}30x-18y=36\\ 30x-20y=10\end{bmatrix}[/tex]
[tex]30x-20y=10[/tex]
[tex]-[/tex]
[tex]\underline{30x-18y=36}[/tex]
[tex]-2y=-26[/tex]
[tex]\begin{bmatrix}30x-18y=36\\ -2y=-26\end{bmatrix}[/tex]
solve for y
[tex]-2y=-26[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-2[/tex]
[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]
[tex]y=13[/tex]
[tex]\mathrm{For\:}30x-18y=36\mathrm{\:plug\:in\:}y=13[/tex]
[tex]30x-18\cdot \:13=36[/tex]
[tex]30x-234=36[/tex]
[tex]30x=270[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}30[/tex]
[tex]\frac{30x}{30}=\frac{270}{30}[/tex]
[tex]x=9[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=9,\:y=13[/tex]
Therefore, the option 'd' is correct.
A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is 2584 square inches, find the width of the frame
Answers
Answer:
The width of the is 4 inches
Step-by-step explanation:
Assume that the width of the frame is x
∵ The width of the fame is x inches
→ That means each dimension will increase by 2x ⇒ x from each side
∵ The portrait has dimensions of 30“ x 60“
∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)
∴ The total area of the portrait plus frame = (30 + 2x)(60 + 2x)
→ Multiply the brackets
∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)
∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²
→ Add the like terms
∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²
∴ The total area of the portrait plus frame = 4x² + 180x + 1800
∵ The total area of the portrait plus frame = 2584 square inches
→ Equate the two right sides of the area
∴ 4x² + 180x + 1800 = 2584
→ Subtract 2584 from both sides
∴ 4x² + 180x + 1800 - 2584 = 0
→ Add the like terms in the left side
∴ 4x² + 180x - 784 = 0
→ Divide all terms by 4 to simplify
∴ x² + 45x - 196 = 0
→ Factorize it to find the value of x
∵ x² + 45x - 196 = (x - 4)(x + 49)
→ Equate the right side by 0
∴ (x - 4)(x + 49) = 0
→ Equate each factor by 0
∵ x - 4 = 0
→ Add 4 to both sides to find x
∴ x = 4
∵ x + 49 = 0
→ Subtract 49 from both sides to find x
∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)
∴ The width of the is 4 inches
A bag contains two coins, one for which the probability of heads is equal to 1 and one for which the probability of heads is equal to p. A coin is selected at random, and three independent tosses of this coin result in three heads. What is the probability that a further independent toss of this coin will produce a head?a. p4/1 + p3.b. p3 - p2/1 + p3.c. p3/1 - p.d. 1/1 + p3.e. 1 + p4/1 + p3.
Answers
Answer: Option E is the correct answer; (1 + p⁴) / (1 + p³)
Step-by-step explanation:
P (3 head) = P(first and 3 heads) + P(second coin and 3 heads)
= (1/2)×1³ + (1/2)× p³ = (1/2) × (1 + p³)
therefore P(first coin given 3 heads) = (1/2)×1³/ ((1/2)×(1 + p³))
= 1 / (1 + p³)
Also P( second coin given 3 heads) = p³ /(1 + p³)
therefore P(4th toss in heads given first 3 are heads) will be;
= P(first and 4th toss heads) + P(second and 4th toss heads)
=(1/( 1 + p³ )) × 1 + p³ / (1+p³) × p
= (1 + p⁴) / (1 + p³)
Therefore Option E is the correct answer
3x+4y=2, find 27x•81v
Answers
Please help. This is a solve for x problem!
Answers
Answer:
3/10 = x or 0.3 = x
Step-by-step explanation:
2.1 / x + 1 4/5 = 3 / 10x
1. first cross multiply and solve it normally:
3 (x + 1 4/5) = (2.1) 10x
3x + 5 2/5 = 21x
-3x -3x
5 2/5 = 18x
3/10 = x or 0.3 = x
these questions are kind annoying to solve because of the fractions, so if you can, use a calculator to solve them! its much easier!
hope this helps!
Answer:
x = 3/10 = 0.3
Step-by-step explanation:
{(2.1)/(x+1 4/5)} = 3/10x
x + 1 4/5 = x + 5/5 + 4/5 = x + 9/5
then:
(2.1)/(x+9/5) = 3/10x
10x*2.1 = 3(x+9/5)
21x = 3x+ 27/5
21x - 3x = 27/5
18x = 27/5
90x/5 = 27/5
90x = 27
x = 27/90
x = 3/10 = 0.3
What number can be replaced with K to make
this a function?
(-5,8) (4,9) (K, 9) (9,9)
A)-5
B)4
C)-9
D)9
Answers
-9 because a function is when an input has only one output
you don’t want to repeat the first numbers in the bracket
and there’s -5, 4 and 9 already so its -9
Hello, I need the steps. I'm kinda confused. Thanks!
Answers
The points: (-3,-1), (6,-7)
(-7+1)/(6+3) = -6/9 = -2/3
Use equation: y = mx + b
y = -2/3x + b
Plot in any point
-1 = -2/3(-3) + b
-1 = 2 + b, b = -3
Final equation in slope intercept form:
Y = -2/3x -3
Answer:
y = -[tex]\frac{2}{3}[/tex] x - 3
Step-by-step explanation:
The general form of the equation of the line (linear equation) is:
y = ax + b
The line passes through (-3, -1) and (6, -7), i.e:
(1) (x=-3, y=-1) is a point that verifies the equation of the line, and
(2) (x=6, y=-7) also verifies the equation.
So we can put up a system of 2 equations to obtain a and b:
y = ax + b
(1) -1 = a (-3) + b
(2) -7 = a (6) + b
______________
substracting (1) - (2) we can obtain a:
-1 - (-7) = a (-3-6) ⇒ 6 = -9 a ⇒ a = -2/3
by replacing a in (1) we can obtain b:
-1 = -2/3 (-3) + b ⇒ -1 -2 = b ⇒ b = -3
so, the equation is: y = ax + b ⇒ y = -2/3 x - 3
Verification: (2) giving x= 6, let's see if y=-7 is obtained:
y = -2/3 6 - 3 ⇒ y = -4 - 3 = 7 ⇒ RIGHT!
please help will give brianliest
Answers
Answer:
I helped
Step-by-step explanation:
you okay do can I get some points cuh
Answer:
with what?? >_>
Cole's soup recipe is shown in the table above. What is the ratio of water to chicken stock? Express the ratio as a fraction in simplest form.
Answers
Answer:
2:3
Step-by-step explanation:
4:6, you would have to divide both sides by 2 to get the simplest answer which is 2:3, hope this helps
Find the variable :
4t + 5.25 = 35.25
Answers
4t + 5.25 = 35.25
4t = 30
t = 30/4 or 7.5
35.25 - 5.25= 30
30/ 4 = 7.5 or 15/2
Just the image below.
Answers
Answer:
Step-by-step explanation:
I'm answering this silly thing only because it seems to have an expected answer
B: is about the only answer you cannot give.
C and D are Both open ended at 15 which doesn't allow you to say that the first acceptable answer is 16
The only answer you can pick is A. The amount starts at 15 and you keep going until you hit 70. That doesn't mean you have to stop. It just means that it represents what he desires to make.
simplify ...........x^4/3+1=3
Answers
Answer:
2 3/4 or 2.75
Step-by-step explanation:
(GIVING BRAINLIEST!!)
Solve the equation using equivalent fractions. SHOW YOUR WORK
4/5 + 3/15 - 2/3
Answers
Answer:
0.3 or 1/3
Step-by-step explanation:
add 4/5 + 3/15=1
then 1-2/3 = 1/3
Answer: 1/3
[tex]\frac{4}{5}+\frac{3}{15}-\frac{2}{3}\\\\=\frac{4}{5}+\frac{3}{3.5}-\frac{2}{3}\\\\=\frac{4}{5}+\frac{1}{5}-\frac{2}{3}\\\\=1-\frac{2}{3}\\\\=\frac{3}{3}-\frac{2}{3}\\\\=1/3[/tex]
Step-by-step explanation:
How many filled sandwich cookies would you need to reach of 1700 mm if you only had one top of the cookie, the stuffing and one bottom of the cookie? Height of top of cookie 3.5 mm height of stuffing 2 mm and height of bottom of cookie 3.5 mm
Answers
Answer:
??
Step-by-step explanation:
Ebony's bank balance first reached $400 on Day 4. The last day her balance was $400 was Day 8. Look at the picture. Brainliest Answer. Only answer if your 100% sure .
Answers
Answer:
It stays true because it stays the same amount so B would be the correct answer.
Step-by-step explanation:
i need help on 23 !!
Answers
Answer:
Step-by-step explanation:
1/4 * 2/3 = 2 / 12 = 1/6
The unit of pencil is what?
Answers
Answer:
In units of measurement of length we use centimeter (cm) to measure. We can use this unit for measuring the length of a pencil, the width of a book etc. but this unit is too big to measure the thicken of a pencil. So we use another unit called millimeter (mm).
Step-by-step explanation:
Helppp please I need help ASAP!!!!!
Answers
Answer:
D
Step-by-step explanation:
The answer is D because the 45 would represent his songs, and 180 would represent the total.
Isabel company offers other programs and incentives to help employees with their savings and expenses.
Answers
Answer:
dependent care FSA
Health FSA
IRA
Step-by-step explanation:
can somone help me please
Answers
Answer:
The slides is 36 and the angle is 180.
Step-by-step explanation:
14.4m+15.6m+6m=36
90+30+50=180
If they ask why it is 180 because when adding all the angles it has to give you a total of 180.
Order the following integers from least to greatest -25,-41,36,28,and16
Answers
find the rate of change (2,15.50) (4,31.00)
Answers
Answer:
The answer is 7.25
Step-by-step explanation:
I suggest you search for, "khan academy slope."
Hope this helps :)
What is 25% of 80 what is the answer fo this question
Answers
25% of 80 is 20
I hope this helps!!!
Answer:
25% of 80 is 20
Step-by-step explanation:
Hamburger meat sells for $6 for every 3 pounds. If Alicia buys 10 pounds of hamburger meat, how much will she pay?
Answers
Every pound is $2
6*3+2
Answer:
20
Step-by-step explanation:
help brainliest will be given 8 only
Answers
b. 26 vehicles
c. 10 vehicles
d. About 27%
Answer:
a)37
b)10
c)0 beacuse if there 11 then they would be speeding and also if it wrond try 10
d)28.571428571429%Step-by-step explanation:
A firm producing poultry feeds finds that the total cost C(x) in dollars of producing and selling x units is given by
C(x) - 20x+100. Management plans to charge $24 per unit for the feed. How many units must be sold for the firm to break even?
Answers
Answer:
Break-even point in units= 25
Step-by-step explanation:
Giving the following information:
Fixed cost= $100
Unitary variable cost= $20
Selling price per unit= $24
To calculate the break-even point in units, we need to use the following formula:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 100 / (24 - 20)
Break-even point in units= 25
False regarding Earnest money
Answers
Answer:
?
Step-by-step explanation:
Answer:
Earnest money is typically in the form of a check.
Step-by-step explanation:
Not everyone writes checks. Can be paid in any form.
1. Adjacent angles are two angles in the same plane with a common
and a common
but no common interior points.
Answers
Answer:
Adjacent angles are two angles in the same plane with a common VERTEX and a common SIDE but no common interior points.
Step-by-step explanation:
Adjacent angles share a common side on the same vertes, but they do not overlap each other.
In the attached image, ∠ABD is adjacent to ∠DBC, but ∠ABC is not adjacent to any of them.