1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f(x)= begincases √x2-1, x ≤ √10 (√10 x-7), √10 < x < 5 sin (π x), 5 ≤ x < 6 x 6 ≤ x ≤ 7 endcases Then the number of points where f(x) is discontinuous in [1,7] is [Note: x denotes fractional part of x.]

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Q. Let $f(x)=\begin{cases} \sqrt{x^{2}-1}, & x \leq \sqrt{10} \\ (\sqrt{10} x-7), & \sqrt{10} < x < 5 \\ \sin (\pi x), & 5 \leq x < 6 \\ \{x\}, & 6 \leq x \leq 7 \end{cases}$
Then the number of points where $f(x)$ is discontinuous in $[1,7]$ is
[Note: $\{x\}$ denotes fractional part of $x$.]

Continuity and Differentiability

Solution:

$f(x)$ is discontinuous in $[1,7]$ at two points viz. $x=5,7$