Question

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

Answer 1

We have f(x) = (x + 1)/2. To find the inverse, set y = (x+1)/2, swap x and y, and solve for y:

x = (y + 1)/2
2x = y + 1
y = 2x − 1

So f⁻¹(x) = 2x − 1 (the first choice).