Question

PLEASE HELP A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.

Answer 1

Part A : see composition process below

Part B :
`Domain=\x\,`

Explanation:

Part A

Let's use the composition of functions to find if they give the identity :
`f(g(x))=x` thus proving they are the inverses of each other:

`f(g(x))=f((5x+1)/(x) )=(1)/((5x+1)/(x)-5) =(1)/((5x+1-5x)/(x)) =(1)/((1)/(x) ) =x`

So we have proved they are the inverses of each other.

Part B

Given that the composition is:

`f(g(x))=(1)/((1)/(x) )`

the Domain must exclude x=0, for which this quotient is undefined.

The Domain is then:

`Domain=\x\,`