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$Let the functions f : R \to R and g : R \to R be defined as:$ $f (x) = \{\begin{array}{cl} x + 2, & x < 0 \\ x^{2}, & x \geq 0 \end{array} and g (x) = \{\begin{array}{cl} x^{3} & x < 1 \\ 3 x - 2, & x \geq 1 \end{array}$ $Then the number of points in R where f \circ g (x) is not differentiable is equal to$

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answer is C.

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Detailed Solution

$f o g (x) = \{\begin{matrix} x^{3} + 3 & ; & x < 0 \\ x^{6} & ; & 0 \leq x < 1 \\ {(3 x - 2)}^{2} & ; & x \geq 1 \end{matrix}$

$\begin{array}{l} At x = 0, discontinuous, hence not differentiable \\ At x = 1, the function is continuous and differentiable \end{array}$

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