verify functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) = x.

Question

f(x)= 5/(2 -x)
g (x) = 2 - 5/x

Answer 1

what's the problem?

f(x) = 5/(2-x) so
f(g) = 5/(2-g)
= 5/(2-[2 - 5/x])
= 5/(2 - 2 + 5/x)
= 5/(5/x)
= 5*x/5
= x

Do likewise for g(f)