Question

If g(x) is the inverse of f(x) and f(x)=4x+12, what is g(x)?

g(x)=12x+4

g(x)=1/4x-12

g(x)=x-3

g(x)=1/4x-3

Answer 1

Answer: Last option.

Step-by-step explanation:

To find the inverse of the function f(x), you must follow the proccedure shown below:

- Rewrite the function,as following:

$y=4x+12$

- Solve for x. Then:

$y-12=4x\\x=\frac{1}{4}y-\frac{12}{4}\\\\x=\frac{1}{4}y-3$

- Now, substitute y with x.

Therefore, you obtain that the inverse function g(x) is the following:

$g(x)=\frac{1}{4}x-3$

Then, the answer is the last option.

Answer 2

Answer:

Last choice is the answer.

Step-by-step explanation:

We have given a function.

f(x) = 4x+12

We have to find the inverse of given function.

Let y  = f(x)

y = 4x+12

Solving for x, we have

x = 1/4y-3

Since, x =  f⁻¹(y)

 f⁻¹(y) =  1/4y-3

Replacing y with x , we have

f⁻¹(x) = 1/4x-3

Given that g(x) = f⁻¹(x)

g(x) = 1/4x-3 which is the answer.