Explanation
Concept:
Finding the Inverse of a Function
1. First, replace f(x) with y
2. Replace every x with a y and replace every y with an x
Example: f(x) = x
Let, f(x) = y => f<sup>-1</sup>(y) = x. Now, determine f<sup>-1</sup>(x) by replacing every y with x
Calculation:
1.f(x) = (1 - x)
Let. f(x) = y => x = f⁻¹(y)
So. y = (1 - x)
Now, replace every x with a y and replace every y with an x
x = (1 - y)
1 + y
(1 + y) x = 1 - y
⇒ x + xy + y = 1
⇒ x + y(x + 1) - 1 = 0
y = (1 - x)/(1 + x)
f⁻¹(x) = (1 - x)/(1 + x) = f(x)
So, f(x) = (1 - x)/(1 + x) is the inverse of itself.
