If $f (x) = | x - 2 |$ and $g (x) = f (f (x))$ , then for $x > 20$ , $g^{'} (x)$ is equal to

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Solution

Since $f (x) = | x - 2 | = x - 2$ for $x > 2$ ,
we have $g (x) = f (f (x)) = f (x - 2) = x - 4$ for $x > 4$ .
Hence $g^{'} (x) = 1$ for $x > 20.$

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