Inverse Functions: Quadratic, square root

Question

Consider the function f(x)=x^2+6 for the domain [0, infinity)

 

Find f^-1(x), where f^-1 is the inverse of f.

 

Also, state the domain of f^-1 in interval notation

Answer 1

f(x) = x² + 6

 

1.  Replace f(x) with y

     y = x² + 6

 

2.  Swap x and y in the equation

     x = y² + 6

 

3.  Solve for y

     y² = x - 6

     y = √(x-6)

 

4.  Replace y with f^-1(x)

     f^-1(x) = √(x-6)

 

Domain:  x-6 ≥ 0

              x ≥ 6

              [6, ∞)