First slide

Derivatives

Question

$If f (x) = | x - 2 |, g (x) = f (f (x)) then for 2 < x < 4, g^{'} (x) is$

Moderate

A

-1
B

1
C

2
D

3

Solution

$f (x) = \{\begin{matrix} x - 2, f o r 2 < x < 4 \\ - (x - 2), f o r x < 2 \end{matrix}$
$∴ g (x) = f (f (x)) = f (x - 2) = |x - 2 - 2| = - (x - 4), 2 < x < 4.$ $∴ g' (x) = - 1$

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