find the inverse

Question

find the inverse of f(x) = Square root of 3x-12:  and whait is the domain of the inverse function.

Answer 1

f(x) = √(3x-12) is a one-to-one function with domain [4,∞) and range [0,∞).  

 

Since f(x) is one-to-one, f(x) has an inverse function with domain [0,∞) and range [4,∞).  

 

Find f^-1(x):  y = √(3x-12)     y²= 3x-12

 

                                        y²+12 = 3x

 

                                              x = (y²+12)/3

 

                Switch x and y to get y = (x²+12)/3

 

                                            f^-1(x) = (x²+12)/3, where x≥0

 

 

                             

 

                                              x