Find the domain of f^-1(x) if f(x)=(x+5)^3

Question

find the domain

Answer 1

The function f(x) = (x + 5)³  

Change f(x) to y.

y = (x + 5)³

Interchange x and y.

x = (y + 5)³

Now solve for y.

x = (y + 5)³

Apply cube root on each side.

∛x = [∛(y + 5)]³

∛x = y + 5

y = ∛x - 5

Replace y by f^-1(x).

f^-1(x) =  ∛x - 5

The domain of f^-1(x) is { x ∈ R : x ≥ 0 }.