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Let f:ℝ→ℝ be ...

Question

Let $f : R \to R$ be a function defined as $f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} 3 (1 - \frac{| x |}{2}) & if & | x | \leq 2 0 & if & | x | > 2 \end{matrix}$

Let $g : R \to R$ be given by $g (x) = f (x + 2) - f (x - 2) .$ If $n$ and $m$ denote the number of points in $R$ where $g$ is not continuous and not differentiable, respectively, then $n + m$ is equal to

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Solution

Clearly $n = 0$ and $m = 4$ .
Hence, $n + m = 4$

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