Inverse functions: Find inverse of y = 2(x + 3)^(1/2) - 1

[Kira]

Please show the steps for the following:

Consider the function y = 2(x + 3)^(1/2) - 1. Find f^(-1)(x).

link to graphic

 

[skeeter]

swap y and x ... solve for y.

x = 2(y + 3)^1/2 - 1

x + 1 = 2(y + 3)^1/2

(x + 1)/2 = (y + 3)^1/2

[(x + 1)/2]² = y + 3

[(x + 1)/2]² - 3 = y = f^-1(x)

don't forget the restrictions on the domain of x for the original function f(x) and the resultant restrictions on x for f^-1(x).

 

[Kira]

Thanks and i wont forget although my teacher has not even covered that yet

I know why i messed up on the graph, i had a root when i was ment to square it.