Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = x - 8 / (x + 7)
g(x) = -7x - 8 / (x - 1)

Answer 1

Replace the function g(x) for the "x" in f(x).

Answer 2

this is for f(g(x)).

Answer 3

$$
f(x) = \cfrac{x-8}{x+7}\\
g(x) = \color{red}{-\cfrac{7x-8}{x-1}}\\
f(g(x)) = \cfrac{
\color{red}{-\cfrac{7x-8}{x-1}}-8}
{\color{red}{-\cfrac{7x-8}{x-1}}+7
}
$$