Let f(x)=⎧⎪⎪⎨⎪⎪⎩{x2},−1≤x<1|1−2x|,1≤x<2(1−x2)sgn(x2−3x−4),2≤x≤4where {k} and sgn(k) denote fractional part function and signum function of k respectively. If m denotes the number of points of discontinuity of f(x) in [−1,4] and n denotes the number of points of non-differentiability of f(x) in (−1,4), then (m+n) is equal to

Let f(x)=⎧⎪⎪⎨⎪⎪⎩{x2},−1≤x<1|1−2x|,1≤x<2(1−x2)s

1.	Let f(x)=⎧⎪⎪⎨⎪⎪⎩{x2},−1≤x<1\|1−2x\|,1≤x<2(1−x2)sgn(x2−3x−4),2≤x≤4where {k} and sgn(k) denote fractional part function and signum function of k respectively. If m denotes the number of points of discontinuity of f(x) in [−1,4] and n denotes the number of points of non-differentiability of f(x) in (−1,4), then (m+n) is equal to
Answer» Let $f (x) = ⎧ ⎪⎪ ⎨ ⎪⎪ ⎩ \begin{matrix} {x^{2}}, & - 1 \leq x < 1 \| 1 - 2 x \|, & 1 \leq x < 2 (1 - x^{2}) sgn (x^{2} - 3 x - 4), & 2 \leq x \leq 4 \end{matrix}$ where ${k}$ and $sgn (k)$ denote fractional part function and signum function of $k$ respectively. If $m$ denotes the number of points of discontinuity of $f (x)$ in $[- 1, 4]$ and $n$ denotes the number of points of non-differentiability of $f (x)$ in $(- 1, 4),$ then $(m + n)$ is equal to