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Thread: inverse function help..

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    Post inverse function help..

    Let $\displaystyle f(x)=-x^{2}-12x+61 , x<-6$. Find a formula for the inverse function.
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    Quote Originally Posted by omibayne View Post
    Let $\displaystyle f(x)=-x^{2}-12x+61 , x<-6$. Find a formula for the inverse function.
    1. Calculate domain and range of f:

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

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

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

    3. Let $\displaystyle f : y = -x^2-12x+61$ then
    $\displaystyle
    u : x = -y^2-12y+61$

    4. Solve this equation for y:

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

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