SOLUTION: I'm having a little trouble solving this one. Given {{{f(x)=-sqrt(x+2)+3}}}, Determine the domain of the inverse {{{f^-1(x)}}}I am getting {{{-x^2+6x-11}}} as the inverse. So the

Question 163985: I'm having a little trouble solving this one.
Given , Determine the domain of the inverse I am getting as the inverse. So the range would be
Am I on the right track here?
Thanks for you help.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function

Replace f(x) with y

Switch x and y

The goal is now to solve for y:

Subtract 3 from both sides

Square both sides

FOIL the left side

FOIL the left side

Combine like terms.

So the solution is which means that the inverse function is where the domain of is and the range is

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