SOLUTION: Hi find the inverse function for the following f(x) = x^2+2x where x is greater than or equal to 0 thanks

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Question 1106122: Hi
find the inverse function for the following
f(x) = x^2+2x where x is greater than or equal to 0
thanks
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
looking for g(x) such that g(f(x)) = x (i.e. if g(x) is the inverse function of f(x) then when it is applied to f(x) it should give us back x.
+f%28x%29+=+x%5E2+%2B+2x+
+f%28x%29+%2B+1+=+x%5E2+%2B+2x+%2B+1+
+sqrt%28f%28x%29+%2B+1%29+=+x%2B1+
+sqrt%28f%28x%29%2B1%29+-+1+=+x+
The LHS is the g(x) we were seeking, just replace "f(x)" with "x", and note that the domain for this x is x%3E=0 because f(x) >= 0 for x>=0:
++highlight%28g%28x%29+=+-1+%2B+sqrt%28x%2B1%29%29 +x%3E=0
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Check: g(f(x)) = +-1+%2B+sqrt%28%28x%5E2%2B2x%29%2B1%29+=+-1+%2B+%28x%2B1%29+=+x+ (ok)
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