SOLUTION: Given f(x)=-sqrt(x)+2, determine the domain of f^-1(x)

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Question 164427: Given f(x)=-sqrt(x)+2, determine the domain of f^-1(x)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's find the inverse.
To find the inverse, first change to x,y notation.
y=-sqrt%28x%29%2B2%29
Then interchange the positions of x and y and solve for y.
highlight%28x%29=-sqrt%28highlight%28y%29%29%2B2
x-2=-sqrt%28y%29
y=%28x-2%29%5E2
The solution for the new y is the inverse function.
f%5E%28-1%29%28x%29=%28x-2%29%5E2
The domain for the inverse looks like all x, (-infinity,infinity).
However, the domain of the original function is bounded by (0,infinity) due to the square root function.
The range of the original function is then (-infinity,2).
The domain of the inverse must match the range of the original function.
Therefore the domain of the inverse function is (-infinity,2).