Practicing Success
Statement - 1: Let $f(x)=[3+4 \sin x]$, where [.] denotes the greatest integer function. The number of discontinuities of $f(x)$ in $[\pi, 2 \pi]$ is 6. Statement - 2: The range of $f$ is $\{-1,0,1,2,3\}$. |
Statement-1 is True, Statement-2 is True; statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is True; statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. |
Statement-1 is False, Statement-2 is True. |
We have, $-1 \leq \sin x \leq 0$ for all $x \in[\pi, 2 \pi]$ $\Rightarrow -4 \leq 4 \sin x \leq 0$ for all $x \in[\pi, 2 \pi]$ $\Rightarrow -1 \leq 4 \sin x+3 \leq 3$ for all $x \in[\pi, 2 \pi]$ $\Rightarrow f(x)=[4 \sin x+3]$ assumes values -1, 0, 1, 2 and 3 when $x \in[\pi, 2 \pi] $ ⇒ Range f = {-1, 0, 1, 2, 3} So, statement- 2 is true. Clearly, there are eight points of discontinuity of $f(x)$ in $[\pi, 2 \pi]$. So statement- 1 is not true. |