Answers
Hi!
We can see here that this is a composition question.
And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).
To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.
[tex]f(x)=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]y=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]x=\frac{e^7^y+\sqrt{3}}{2}[/tex]
[tex]2x=e^7^y+\sqrt{3}[/tex]
[tex]e^7^y=2x-\sqrt{3}[/tex]
[tex]7y=ln(2x-\sqrt{3})[/tex]
[tex]y=\frac{ln(2x-\sqrt{3})}{7}[/tex]
Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.
[tex]g(f(x))[/tex]
[tex]g(\frac{e^7^x+\sqrt{3}}{2})[/tex]
[tex]\frac{ln(2(\frac{e^7^x+\sqrt{3}}{2})-\sqrt{3}}{7}[/tex]
2s cancel.
[tex]\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}[/tex]
The natural log and e cancel.
[tex]\frac{7x+\sqrt{3}-\sqrt{3}}{7}[/tex]
[tex]\sqrt{3}[/tex]s cancel.
[tex]\frac{7x}{7}[/tex]
7s cancel.
[tex]x[/tex]
Hope this helps!
Related Questions
I need help on this homework
Answers
Answer:
Tn=a(n-1)d
T50=261(50-1)-5
T50=12784
Someone please help with this
Answers
Answer:
A
Step-by-step explanation:
I said so
Answer:
C. They are similar triangles.
Step-by-step explanation:
they have the same angle measures, but not the same side lengths. so they are similar but not congruent.
The number of students who picked each subject is shown.
What percent of students did not pick History?
Answers
Answer: 90% of students did NOT choose history.
Step-by-step explanation:
Art - 32.5%
Spanish - 7.5%
ELA - 10%
Math - 15%
Science - 25%
When added altogether each subject equals 90%, leaving the other 10 percent history. 90% is our answer since that is the number of people that voted for subjects other than history.
Hope This Helped, Have A Great Day!
Which expression is equivalent to 4m + 3?
A. 2(2m + 3)
B. -2(-2m + 3)
C. (-2)m - (-1)3 + (-2)2m
D. (-2)m - (-3)1 + (2)3m
Answers
Answer:
D)
Step-by-step explanation:
4m+3
Please help me solve “Expand log3 4x”
Answers
Answer:
Look below.
Step-by-step explanation:
Log3^4x
4xLog3 ------> To expand you would take the exponent and put infront of Log
This is the answer if its expanded. The question was sort of scarce so if this is wrong im sorry.
The expansion of the given logarithm [tex]\mathbf{Log_3 (4x^2)}[/tex] is [tex]\mathbf{= 2log_3(2)+2log_3(x)}[/tex]
What is the expansion of the logarithm?A Logarithm is an exponent to which a base must be raised in order to result in a given number. The expansion of the logarithm takes a predictable approach and set guidelines.
Using the set formula for solving logarithms;
[tex]\mathbf{log_a(x^n) = n \ log_a \ x}[/tex]
Let's assume that the correct equation given is:
[tex]\mathbf{=Log_3 (4x^2)}[/tex]
Using the above formula, we have
[tex]\mathbf{= 2 Log_3 (4x)}[/tex]
By expansion;
[tex]\mathbf{= 2log_3(2)+2log_3(x)}[/tex]
Learn more about logarithm here:
https://brainly.com/question/237321
Farah harvests 20 pounds of tomatoes from her garden. She needs 4 4/5 pounds to make a batch of soup. Additionally, if she uses 5.6 pounds of tomatoes to make spaghetti sauce, how many batches of soup can Farah make?
Answers
Answer:
1 batch
Step-by-step explanation:
Farah needs 4 and 4/5 pounds of tomatoes & and additional 5 and 3/5 pounds of tomatoes to make soup.
4.8 + 5.6 = 10.5 pounds per soup
10.5*2 = 21 > 20 pounds
Farah would need one more pound of tomatoes in order to make 2 batches of soup. Therefore she can only make 1 batch.
f(x) = –x^2 – 4x
Find f(-1)
Answers
Answer:
3
Step-by-step explanation:
Evaluate F(x) = –x^2 – 4x by substituting -1 for x:
F(-1) = –(-1)^2 – 4(-1)
This becomes:
F(x) = –1 + 4 = 3
how do i put that on a line?please help me.
Answers
9. If ground beef costs $4.98 for 3 pounds, then what is the unit rate (cost per
pound)?
(a) What is the unit rate (cost per pound)? Don't forget units!
(b) Explain how you found the unit rate.
Explanation:
Answers
Answer:
1.66 pounds
Step-by-step explanation:
4.98 dollars divided by 3 pounds
PLEASE HELP QUICKLY I WILL MARK YOU BRAINLIEST.
Mr. Rector and Ms. Mitchell are grading papers. Mr. Rector can grade 24 papers in 10 minutes. Ms. Mitchell can grade 30 papers in 8 minutes. How many more papers per minute can Ms. Mitchell grade?
Answers
Answer: 1.35
Step-by-step explanation:
Answer:
1.35
Step-by-step explanation:
We need to identify our independent variables and dependent variables.
The number of papers graded depend on the amount of time.
The amount of time is the independent variable
The papers graded depends us the dependent variable
Divide the independent variable by the dependent variable to find papers per minute
For Ms.Mitchell the papers per minute is
For Mr.Rector, the papers per minute is
Subtract 2.4 from 3.75.
The answer is 1.35
The Martinez Family has driven 240 miles so far. Their total trip is 300 miles. What percentage of the trip have they already driven
Answers
Answer:
90%
Step-by-step explanation:
Answer:
80%
Step-by-step explanation:
I thought I had $35 in my bank account.
When I checked my balance, I actually
had $75. Aaayyyyeeee!!! What was my
percent error?
Answers
your awnser will be 100 because if
what is 30 = –5d – 5
Answers
Answer:
-7
Step-by-step explanation:
30=-5d-5
-5d=30+5
-5d=35
d=35/-5
d=-7
If your answer is right ill give brainliest!!!
Answers
Answer:
I don't know I am a babysitter too :)
I need the answer for the question -4(x-10)+8 for my homework please.
Answers
Answer:
i think the answer is
-4x+48
plsssssssss help I really need to do this I will give brainliest to anyone who solves
Answers
Answer:
MSP: 6a/2
CUB: ab/2
ABC: 20 square centimeters
KDR: 5x cm * 3x cm / 2
Step-by-step explanation:
MSP: 6 x a divided by 2
CUB: a x b divided by 2
ABC: 8 x 5 divided by 2
KDR: 5xcm * 3xcm divided by 2
When solving (5/3)^-2 What do you do first?
Answers
Answer:
steps:
(5/3)^-21 / (5/3)² (first turn the negative exponent to positive)1 × 3²/5² (division by a fraction turned to multiplication by the multiplicative inverse of (5/3)²)3²/5²9/25Suppose the inflation rate is 7% per year. How much would a $24 pair of
sneakers cost in 8 years? Estimate your answer to 2 places after the decimal.
Tine your answer
Answers
$1.68 x 8 = $13.44
$13.44 + $24.00 = $37.44
$37.44 would be how much they cost in 8 years
Pythagorean therom HELPPPO
Answers
Answer:
6
Step-by-step explanation:
change up the formula so:
sqrt (10^2-8^2)= 6
The graph of a function f is shown below. Find f(-1).
Answers
A map of a highway has a scale of 2 inches=45 miles. The length of the highway on the map is 9 inches. There are 7 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch=30 miles. How far apart are the rest stops on the new map?
Answers
Answer:
25.7 miles apart
Step-by-step explanation:
this may not be right, if its not im sory
Fill in the blank
10:18=________:9
Answers
Answer:
the answer to the blank is 5
(just in case you're confused) the answer is 5:9
Step-by-step explanation:
draw a number line and make ticks that are 1cm apart from-6 to7
Answers
What is the common ratio for geometric sequence: 5,15,45,135 ?
Answers
Answer:
the common ratio is 3
Step-by-step explanation:
to solve for the common ratio, I like to take the second term and divide it by the first term
15/5 = 3
then I will check the rest of the terms
15*3 = 45
45*3 = 135
It looks like the common ratio is correct!
what is the slope of y=-4x-8
Answers
Answer:
-4
Step-by-step explanation:
y = mx + b
Answer:
-4
Step-by-step explanation:
y=mx+b
m is slope
b is y-intercept
So you line y=mx+b and y=-4x-8
-4 is replacing m so -4 is the slope
Hope this helps!
Which statement describes the end behavior of the function f(x) = 8|x − 1| + 13?
A.
As x approaches negative infinity, f(x) approaches negative infinity.
B.
As x approaches negative infinity, f(x) approaches positive infinity.
C.
As x approaches positive infinity, f(x) approaches negative infinity.
D.
As x approaches positive infinity, f(x) is no longer continuous.
Answers
The statement that describes the end behavior of the function f(x) = 8|x − 1| + 13 is:
As x approaches positive infinity, f(x) approaches negative infinity.C.
Let's analyze the function.
The function f(x) = 8|x − 1| + 13 involves the absolute value of x − 1, which means that the expression inside the absolute value will always be non-negative.
x approaches positive infinity, the value of x − 1 also approaches positive infinity.
Since the absolute value of a positive number is equal to the number itself, we can simplify the expression to f(x) = 8(x − 1) + 13.
As x approaches positive infinity, the term 8(x − 1) becomes larger and larger, making f(x) approach negative infinity.
The constant term 13 does not have a significant impact on the end behavior as x becomes increasingly large.
For similar questions on function
https://brainly.com/question/25638609
#SPJ8
What is the equation of the yellow line
Answers
Answer:
y = -[tex]\frac{5}{3}[/tex] x -2
Step-by-step explanation:
The line is going down to the right so it has the negative slope, with a y- intercept of (0, -2) and a slope of m = rise/run = -5/3
Erika decided to compare her observations to the average annual trend, which shows the water rising 1.8 mm/year. Remember, she used 6.2 years as her time period. Explain how she would calculate the difference between how much the water level fell in the part of the river she observed.
Answers
Answer:
Change in water level over thr period Given is 11.16 mm
Step-by-step explanation:
The change in water level. In the part of the river observed will be ;
Water level. = The rate of change in water level per year * period
Rate of change in water level = 1.8mm /year
Number of years = 6.2
The change in water level is thus :
1.8 mm / year * 6.2 years
= (1.8 mm / year * 6.2
= 11.16 mm
The function table below represents the linear function y = 4x – 3. Which answer represents the outputs of the function table
Answers
Answer:
Here we can not see the options, so i will answer in a general way.
When we have a function y = f(x), we define:
x as the input
y as the output.
so f(x) is some kind of "machine", in wich we put an input x, and the "machine" does something and returns an output y.
In, this case, we have:
y = f(x) = 4*x - 3
then if we give this function different inputs, we will get different ouputs.
for example, if we use the input x = 0, then the output is:
y = f(0) = 4*0 - 3 = -3
Then if we made a table for inputs and outputs, we will have the data:
[tex]\left[\begin{array}{ccc}inp&out\\x&y\\0&-3\end{array}\right][/tex]
We can rewrite this table in a general way as:
[tex]\left[\begin{array}{ccc}inp&out\\x&4*x - 3\end{array}\right][/tex]
This means that for every input x, the output is always 4*x - 3.
To complete this type of tables, we usually use different values of x, for example here I will use some different ones:
y = f(3) = 4*3 - 3 = 12 - 3 = 9
y = f(10) = 4*10 - 3 = 40 - 3 = 37
y = f(-1) = 4*-1 - 3 = -4 - 3 = -7
Then we will have a table like:
[tex]\left[\begin{array}{ccc}inp&out\\3&9\\10&37\\-1&-7\end{array}\right][/tex]
Concluding, the thing that will always represent the output of our function is: 4*x - 3.
Leanne has 64 candies. She buys 4 more packages of
candies that each have 8 candies in them.
How many candies does Leanne have now?
Answers
Answer:
96
Step-by-step explanation:
yeee