inverse function help..

**omibayne** · November 16th 2008, 09:21 PM

Let $f(x)=-x^{2}-12x+61 , x<-6$ . Find a formula for the inverse function.

**earboth** · November 16th 2008, 10:19 PM

Originally Posted by omibayne

Let $f(x)=-x^{2}-12x+61 , x<-6$ . Find a formula for the inverse function.

1. Calculate domain and range of f:

$D_f=(-\infty, -6)$ and $R_f=(-\infty, 97)$

2. Therefore the domain and range of the inverse function u is:

$D_u=(-\infty, 97)$ and $R_u=(-\infty, -6)$

3. Let $f : y = -x^2-12x+61$ then
$<br /> u : x = -y^2-12y+61$

4. Solve this equation for y:

$y = -6\pm\sqrt{97-x}$ . And since y must be smaller than -6 the equation of the inverse function is:

$u(x) = -6-\sqrt{97-x}$

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