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Calculus/inverse of function

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Expert: - 5/25/2010


Question
Find a formula for the inverse of the function:
f(x) = sqrt((x^2)+7x)   where x>0

f-1(x) = ???

Answer
The best way to do this is to replace f(x) with y, and then solve for x.

That is, y = √(x²+7x).  Squaring both sides gives y² = x² + 7x.

Subtracting y² from both sides gives 0 = a parabola with -y² as the constant.

To solve, use the quadratic formula with a = 1, b = 7, and c = -y².

In the middle of the quadratic formula is a ±.  Test both the + and the - to see if they work.
This needs to be done since we squared both sides to start with and one may be an extraneous solution.

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