Question

For the function f, of, x, equals, 2, left parenthesis, x, plus, 10, right parenthesisf(x)=2(x+10), 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 fraction, left parenthesis, x, plus, 10, right parenthesis, divided by, 2, end fractionf
−1
(x)=
2
(x+10)
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, divided by, 2, end fraction, minus, 10f
−1
(x)=
2
x
​
−10
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 2, left parenthesis, x, minus, 10, right parenthesisf
−1
(x)=2(x−10)
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 2, x, minus, 10f
−1
(x)=2x−10

Answer 1

f(x) = 2(x+10) = 2x + 20. Let y = 2x + 20. Swap x and y: x = 2y + 20. Solve for y: y = (x - 20)/2 = x/2 - 10.

So f^{-1}(x) = x/2 - 10 (the option x/2 − 10).