For the function f, of, x, equals, start fraction, x, cubed, plus, 8, divided by, 9, end fractionf(x)=

9
x
3
+8

, find f, to the power minus 1 , left parenthesis, x, right parenthesisf
−1
(x).
Answer
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, cube root of, 9, x, minus, 8, end cube rootf
−1
(x)=
3

9x−8


f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, cube root of, 9, x, end cube root, minus, 8f
−1
(x)=
3

9x

−8
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 9, cube root of, x, minus, 8, end cube rootf
−1
(x)=9
3

x−8


f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 9, left parenthesis, cube root of, x, end cube root, minus, 8, right parenthesisf
−1
(x)=9(
3

x

−8)

1 answer

To find the inverse function f1(x) of the given function f(x)=x3+89, we will follow the steps to isolate x in terms of y.

  1. Start with the equation: y=x3+89

  2. Multiply both sides by 9 to eliminate the fraction: 9y=x3+8

  3. Subtract 8 from both sides: 9y8=x3

  4. Take the cube root of both sides to solve for x: x=9y83

  5. To express the inverse function, switch x and y: f1(x)=9x83

Now, let's look at the multiple-choice answers:

  1. f1(x)=9x83
  2. f1(x)=9x38
  3. f1(x)=9x38
  4. f1(x)=9(x38)

The correct answer is the first option:

f1(x)=9x83