Question

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

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}\]

Answer 2

i mean \[y=\sqrt{x+16}\]

Answer 3

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

Answer 4

oh yeah my bad =.="

Answer 5

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

Answer 6

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
\[f^{-1}(x)=\sqrt{x+16}\]