Let f(x) = x2 – 16. Find f–1(x).
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Question

Let f(x) = x2 – 16. Find f–1(x).
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anonymous · Answer

find the inverse of the function. replace y to x and x to y
$$y=x ^{2}-16$$
$$x=y ^{2}-16$$
Look for new y
$$x+16=y ^{2}$$
then take square root to look for y alone
we have $$y=\sqrt{x-16}$$

anonymous · Answer

i mean $$y=\sqrt{x+16}$$

anonymous · Answer

actually, since $f(x)=x^2-16$ is not a one to one function it does not have an inverse

anonymous · Answer

oh yeah my bad =.="

anonymous · Answer

you could write $y=\pm\sqrt{x+16}$ but this is not a function precisely because of the $\pm$

anonymous · Answer

if you like you can restrict the domain of $f$ and then it would have an inverse that is a function. for example you could say "Let $f(x)=x^2-16$ for $x\geq 0$ and then the inverse would be 
$$f^{-1}(x)=\sqrt{x+16}$$