Find the f inverse of x, if f(x) = 1 + √ x - 2.

Question

f(x) = 1 + √x-2

f^-1(x) = ?

Answer 1

Domain f = [2, ∞)   Range f = [1, ∞)

 

Let y = f(x):  y = 1 + √(x-2)

 

Switch x and y:  x = 1 + √(y-2)

 

Solve for y:  √(y-2) = x - 1

 

                      y - 2 = (x-1)²

 

                          y = (x-1)² + 2 = f^-1(x), where x≥ 1 [Since domain f^-1(x) = Range f(x)]

 

                      y - 2 = (x-1)