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
Attempt 1 out of 2
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start root, start index, 7, end index, x, minus, 1, end rootf
−1
(x)=
7

x−1
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, left parenthesis, x, plus, 1, right parenthesis, to the power 7f
−1
(x)=(x+1)
7

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start root, start index, 7, end index, x, plus, 1, end rootf
−1
(x)=
7

x+1
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, x, to the power 7 , plus, 1f
−1
(x)=x
7
+1

Answer 1

Let y = x^7 − 1. Solve for x:
y + 1 = x^7 ⇒ x = (y + 1)^(1/7).

Thus the inverse is f⁻¹(x) = (x + 1)^(1/7). (Domain and range: all real numbers.)