Answer:
- f(g(x)) = x-5
- the functions are NOT inverses
Step-by-step 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.
