Composition of functions

Question

For the function f, use composition of functions to show that f^-1 is as given.

1) f(x)=∛x+1 , f^-1(x)= x^3-1

Answer 1

f comp f_inv =

cube_root ( (x^3 - 1) + 1 ) = cube_root ( x^3) = x

f_inv comp f =

(cube_root(x+1))^3-1 =

x+1-1 =x

Since both compositions of f and the inverse

result in the identity function y=x, the inverse

is correct