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How do you determine whether the function $f (x) = \sqrt{x - 2}$ $f(x)=sqrt(x-2)$ has an inverse and if it does, how do you find the inverse function?

1 Answer

Sep 8, 2017

$f (x) = \sqrt{x - 2}$ $f(x)=sqrt(x-2)$ has an inverse, namely $¯ ¯¯¯¯¯ ¯ f (x) = x^{2} + 2$ $barf(x)=x^2+2$

Explanation:

If $f (x) = \sqrt{x - 2}$ $f(x)=sqrt(x-2)$
then
$XXX f^{2} (x) = x - 2$ $color(white)("XXX")f^2(x)=x-2$
and
$XXX x = f^{2} (x) + 2$ $color(white)("XXX")x=f^2(x)+2$

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