Question

Hello! I need some help with this homework question, please? The question is posted in the image below. Q22

Answer 1

Given the following functions

`\begin{gathered} f(x)=3x-12 \\ g(x)=(x)/(3)+4 \end{gathered}`

We want to find their compositions. Evaluating a function means finding the value of the function that corresponds to a given value of x. Compose two functions is the same as "evaluating" the inside function on the outside function. To do this, simply replace all the x variables with the expression of the inside function.

For the first composition, we have

`f(g(x))=f((x)/(3)+4)=3((x)/(3)+4)-12=x+12-12=x`

There are no restrictions on this function, therefore, the domain is all real numbers.

For the second composition, we have

`g(f(x))=g(3x-12)=((3x-12))/(3)+4=x-4+4=x`

There are no restrictions on this function, therefore, the domain is all real numbers.

Since

`f(g(x))=g(f(x))=x`

Those functions are the inverse of each other.