Chemistry NCERT Exemplar Solutions Class 12th Chapter Five Maths Class 11th Relations and Functions

Let [t] denote the greatest integer $\leq t .$ The number of points where the function f(x) = $[x] | x^{2} - 1 |$ + sin $(\frac{π}{[x] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is__________.

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

$f (x) = {\begin{cases} - 2 x^{2} + 3, - 2 < x < - 1 \\ x^{2}, - 1 \leq x < 0 \\ \frac{\sqrt[]{3}}{2} - 1, 0 \leq x < 1 \\ x^{2} - 3 + \frac{1}{\sqrt[]{2}}, 1 \leq x < 2 \end{cases}$

$f (- 1^{-}) = f (- 1^{+}) = f (- 1) = 1$

$f (1^{+}) = f (1) = \frac{1}{\sqrt[]{2}} - 2$

Points of discontinuity

x = 0, 1

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Let [t] denote the greatest integer $\leq t .$ The number of points where the function f(x) = $[x] | x^{2} - 1 |$ + sin $(\frac{π}{[x] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is__________.

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Let [t] denote the greatest integer ≤ t . The number of points where the function f(x) = [ x ] | x 2 − 1 | + sin ( π [ x ] + 3 ) − [ x + 1 ] , x ∈ ( − 2 , 2 ) is not continuous is__________.

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Let [t] denote the greatest integer $\leq t .$ The number of points where the function f(x) = $[x] | x^{2} - 1 |$ + sin $(\frac{π}{[x] + 3}) - [x + 1], x \in (- 2, 2)$ is not continuous is__________.