Question

For the function f, of, x, equals, start fraction, left parenthesis, x, plus, 2, right parenthesis, divided by, 5, end fractionf(x)=
5
(x+2)
​
, find f, to the power minus 1 , left parenthesis, x, right parenthesisf
−1
(x).

Answer 1

Let y = f(x) = (x + 2)/5. Solve for x:

5y = x + 2
x = 5y − 2.

Swap x and y to get the inverse function:

f⁻¹(x) = 5x − 2.

(You can check: f(f⁻¹(x)) = ((5x−2)+2)/5 = x.)