Write the range of the function f(x)= [x], where - 4 4 - Vidyadip

Question

Write the range of the function $\text{f(x)}=\sin[\text{x}],$ where $\frac{-\pi}{4}\leq\text{x}\leq\frac{\pi}{4}$

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Answer

We have,
$\text{f}(\text{x})=\sin[\text{x}], $ where $\frac{-\pi}{4}\leq\text{x}\leq\frac{\pi}{4}$
Now,
$[\text{x}]= \begin{cases}0, & \text{x} = \frac{\pi}{4}\\-1, &\text{ x} = \frac{-\pi}{4}\end{cases}$
$\therefore \sin\text{{x}} = \begin{cases}0, & \text{x} = \frac{\pi}{4}\\-\sin1, &\text{ x }=\frac{-\pi}{4}\end{cases}$
$\therefore$ Range $(\sin[\text{x}])= \{{-\sin 1,0,\sin1}\}$

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