Are g(x) and f(x) inverses of each other? show all work always and explain in
words as you go. *
g(x)=4-3/2x
f(x)=1/2x+3/2

No,   and are not inverses of each other.

Step-by-step explanation:

Given functions:

To tell whether and are inverse of each other.

Solution:

If   and are inverse of each other, then:

  or  

Thus, to check if they are inverse of each other, we will find inverse of function and see if it is =

We have:

In order to find inverse we will replace with

Then we switch and

Then, we solve for

Subtracting both sides by 4.

Multiplying both sides by 2.

Using distribution:

Dividing both sides by -3.

Thus inverse of function can be given as:

Since , hence they are not inverse functions of each other.