Question

Use compositions to verify that g and g^-1 are in fact inverses.

g(x): 1/x+2
g^-1(x): 1/x - 2

Answer 1

as written there, they are not inverses

proof by counter example: since g(1) = 3 , but g^-1(3) = -5/3 != 1

Explanation:

g(g^-1(x)) == x if they are indeed inverses

1/(1/x -2) + 2 = x/(1-2x) + 2 != x so, they are not inverses