Question

For the function f, of, x, equals, x, to the power 7 , minus, 1f(x)=x
7
−1, find f, to the power minus 1 , left parenthesis, x, right parenthesisf
−1
(x).

Answer 1

Let y = f(x) = x^7 − 1. Solve for x:

y + 1 = x^7 ⇒ x = (y + 1)^{1/7}.

Thus the inverse function is
f⁻¹(x) = (x + 1)^{1/7} = √[7]{x + 1},

defined for all real x (the seventh root is single-valued on R).