Problem

Let
\[
f(x)=(x-6)^{2}
\]
Find a domain on which $f$ is one-to-one and non-decreasing.
Find the inverse of $f$ restricted to this domain
\[
f^{-1}(x)=
\]
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Answer

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Answer

\(\boxed{y = \sqrt{x} + 6}\)

Steps

Step 1 ：\(y = (x-6)^2\)

Step 2 ：\(x = (y-6)^2\)

Step 3 ：\(\sqrt{x} = y - 6\)

Step 4 ：\(\boxed{y = \sqrt{x} + 6}\)

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