Question

How do I solve this question?

Answer 1

c

Explanation:

Work out the composition and see what you get.

`(f\circ g)(x)=f(g(x))=f(7x+10)=((7x+10)-10)/(7)=(7x)/(7)=x`

This is your first clue that the functions are inverses of each other, so we expect that g(f(x)) = x will be true, too. We can work that out to confirm it.

`(g\circ f)(x)=g(f(x))=g\left((x-10)/(7)\right)=7\left((x-10)/(7)\right)+10\\\\=(x-10)+10=x`

So, the appropriate choice is as shown below.