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

Algebra ->  Functions -> 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       Log On


   

Question 163985: I'm having a little trouble solving this one.
Given f%28x%29=-sqrt%28x%2B2%29%2B3, Determine the domain of the inverse f%5E-1%28x%29I am getting -x%5E2%2B6x-11 as the inverse. So the range would be x%3E=-2
Am I on the right track here?
Thanks for you help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-sqrt%28x%2B2%29%2B3 Start with the given function


y=-sqrt%28x%2B2%29%2B3 Replace f(x) with y


x=-sqrt%28y%2B2%29%2B3 Switch x and y


The goal is now to solve for y:

x-3=-sqrt%28y%2B2%29 Subtract 3 from both sides


%28x-3%29%5E2=y%2B2 Square both sides


x%5E2-6x%2B9=y%2B2 FOIL the left side


x%5E2-6x%2B7=y%2B2 FOIL the left side


x%5E2-6x%2B7=y Combine like terms.


So the solution is y=x%5E2-6x%2B7 which means that the inverse function is f%5E-1%28x%29=x%5E2-6x%2B7 where the domain of f%5E-1%28x%29 is x%3C=3 and the range is y%3E=-2