F(x) = square root x - 5 find f^-1

1 answer:

6 0

As you may know, to get the "inverse relation" of any expression, we start off by doing a quick switcharoo on the variables, and then we solve for "y".

$\bf \stackrel{f(x)}{y}=\sqrt{x-5}\qquad \boxed{x}=\sqrt{\boxed{y}-5}\impliedby \textit{let's square both sides}
\\\\\\
(x)^2=(\sqrt{y-5})^2\implies x^2=y-5\implies x^2+5=\stackrel{f^{-1}(x)}{y}$

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