Question

Find f(g(x)) for the functions f(x) = (x+1)^3 -5 and g(x) = ^3sqrt(x) -1

are these functions inverses?

Answer 1

• f(g(x)) = x-5
• the functions are NOT inverses

Explanation:

Substitute g(x) for x in f(x) and evaluate:

f(g(x)) = f(x^(1/3) -1)

= ((x^(1/3) -1) +1)^3 -5

= (x^(1/3))^3 -5

= x^(3/3) -5

f(g(x)) = x -5

This is confirmed by a graphing calculator. (See attached.)

If the functions were inverses, the value of f(g(x)) would be x. It is not, so the functions are not inverses.