1. ## inverse function help..

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

2. 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
$
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:

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