Question

For the function f, of, x, equals, 2, x, plus, 6f(x)=2x+6, 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, x, divided by, 2, end fraction, minus, 6f
−1
(x)=
2
x
​
−6
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 2, left parenthesis, x, minus, 6, right parenthesisf
−1
(x)=2(x−6)
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, left parenthesis, x, minus, 6, right parenthesis, divided by, 2, end fractionf
−1
(x)=
2
(x−6)
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, left parenthesis, x, plus, 6, right parenthesis, divided by, 2, end fractionf
−1
(x)=
2
(x+6)

Answer 1

Let y = 2x + 6. Swap x and y and solve for y:
x = 2y + 6
x − 6 = 2y
y = (x − 6)/2

So f⁻¹(x) = (x − 6)/2. (This is the third choice.)