Question

For the function f, of, x, equals, left parenthesis, x, minus, 4, right parenthesis, cubedf(x)=(x−4)
3
, 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, cube root of, x, end cube root, minus, 4f
−1
(x)=
3

x
​
−4
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, left parenthesis, x, plus, 4, right parenthesis, cubedf
−1
(x)=(x+4)
3

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, cube root of, x, plus, 4, end cube rootf
−1
(x)=
3

x+4
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, cube root of, x, end cube root, plus, 4f
−1
(x)=
3

x
​
+4

Answer 1

Let y = (x − 4)^3. Swap x and y: x = (y − 4)^3. Take cube roots: ∛x = y − 4, so y = ∛x + 4.

Thus f⁻¹(x) = ∛x + 4 (the option "cube root of x plus 4").