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

$y = \sqrt{x} + 6$

Steps

Step 1 ： $y = (x - 6)^{2}$

Step 2 ： $x = (y - 6)^{2}$

Step 3 ： $\sqrt{x} = y - 6$

Step 4 ： $y = \sqrt{x} + 6$

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