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

Question

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

✓

Answer

From the given question , we can write,
$\begin{array}{l}f(x)=\sin (x) \\ -\frac{\pi}{4} \leq x \leq \frac{\pi}{4} \\
\operatorname{Sin}\left[-\frac{\pi}{4}\right]=\sin (-1) \\ =-\sin 1 \\ \sin 0=0 \\ \sin
\frac{\pi}{4}=\sin 0 \\ =0\end{array}$
using properties of greatest integer function
(1) = 1. (0.5) = 0. (0.5) = -1
Hence, R(f) = -( sin 1.0)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Model Paper 5→Model Paper 5 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the sum of the following geometric series:
$\text{x}^3,\text{x}^5,\text{x}^7,\ ...\ \text{to n terms}$

Find the equations to the circles which pass through the origin and cut off equal chords of length 'a' from the straight lines y = x and y = -x.

Reduce the equation $x-\sqrt{3} y+8=0$ into normal form. Find the perpendicular distance from the origin and angle between the perpendicular and the positive X-axis.

Evaluate:
$\lim\limits_{\text{x} \rightarrow\frac{\pi}{4}}\frac{\sin\text{x}-\cos\text{x}}{\text{x}-\frac{\pi}{4}}$

Reduce the following equations to the normal form and find p and $\alpha$ in each case:
$\text{x}+\sqrt{3}\text{y}-4=0$

Express the following complex numbers in the standard form a + ib:
$\frac{5+\sqrt{2}\text{i}}{1-\sqrt{2}\text{i}}$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-1}\frac{\text{x}^3+1}{{\text{x}+1}}$

How many teterms are there in the A.P. $-1,-\frac{5}{6},-\frac{2}{3},-\frac{1}{2},\ ...,\frac{10}{3}?$

Show that if $\text{x}^2 + \text{y}^2 = 1,$ then the point $\Big(\text{x, y},\sqrt{1-\text{x}^2-\text{y}^2}\Big)$ is at a distance 1 unit from the origin.

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm $\left( {use\;\pi = \frac{{22}}{7}} \right)$