Question

For the function f, of, x, equals, start fraction, x, divided by, 5, end fraction, plus, 5f(x)=
5
x
​
+5, 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, 5, x, minus, 5f
−1
(x)=5x−5
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, left parenthesis, x, minus, 5, right parenthesisf
−1
(x)=5(x−5)
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, divided by, 5, end fraction, minus, 5f
−1
(x)=
5
x
​
−5
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, left parenthesis, x, plus, 5, right parenthesisf
−1
(x)=5(x+5)

Answer 1

Let y = f(x) = x/5 + 5. Solve for x:

y − 5 = x/5 → x = 5(y − 5) = 5y − 25.

Swap variables: f⁻¹(x) = 5x − 25 = 5(x − 5).

So the correct choice is f⁻¹(x) = 5(x − 5).