SOLUTION: Please help me solve this equation: Consider f(x) = x2 + 3, x < 0. What is the inverse of this function?

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Question 967940: Please help me solve this equation:
Consider f(x) = x2 + 3, x < 0. What is the inverse of this function?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe you meant f%28x%29=x%5E2%2B3, for x%3C0 ?
You want the inverse of f.

Let g(x) be the inverse function of f(x).
g%28f%28x%29%29=f%28g%28x%29%29=x.

%28g%28x%29%29%5E2%2B3=x
%28g%28x%29%29%5E2=x-3
g%28x%29=0%2B-+sqrt%28x-3%29, for g%28x%29%3C0 only. The negative branch of this is required; so this means what the really needed answer is:

highlight%28g%28x%29=-sqrt%28x-3%29%29 AND x%3E=3 if staying with real number solutions.