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

Last choice is the answer.

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.

Answer 2

Answer: Last option.

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=(1)/(4)y-(12)/(4)\\\\x=(1)/(4)y-3`

- Now, substitute y with x.

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

`g(x)=(1)/(4)x-3`

Then, the answer is the last option.