The domain of function f(x)= ^ -1 x+ x is- - Vidyadip

Question

The domain of function $f(x)=\sin ^{-1} x+\cos x$ is-

✓

Answer

(A)
$[-1,1]$
Function $\sin ^{-1} x$ has domain $D _1=[-1,1]$ and function $\cos x$ has domain $D _2= R$
$\therefore$ Domain of $f(x)=\sin ^{-1} x+\cos x$ is $= D _1 \cap D _2=$ $[-1,1] \cap R =[-1,1]$
Hence correct option is (A).

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 "M.C.Q (1 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

For $\text{x, }\epsilon\text{ R},\text{f}(\text{x})=\mid\log2-\sin\text{x}\mid$ and g(x) = f(f(x)) then:

$\text{g}'(0)=\cos (\log2)$
$\text{g}'(0)=-\cos (\log2)$
$\text{g }\text{is diffrerentible at x = 0 and }\text{g}'(0)=-\sin(\log2)$
$\text{g }\text{is diffrerentible at x = 0 }$

The direction ratios of the line joining the points A(4, −3, 7) and B(1, 3, 5) are:

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

$\int\limits^\frac{\pi}{2}_0\frac{1}{2+\cos\text{x}}\text{ dx}$ equals:

$\frac{1}{3}\tan^{-1}\Big(\frac{1}{\sqrt{3}}\Big)$
$\frac{2}{\sqrt{3}}\tan^{-1}\Big(\frac{1}{\sqrt{3}}\Big)$
${\sqrt{3 }}\tan^{-1}\big({\sqrt{3}}\big)$
$2{\sqrt{3 }}\tan^{-1}{\sqrt{3}}$

$\int_{0}^{\infty}\frac{1}{1+\text{e}^\text{x}}\text{dx}=$

$\log2$
$-\log2$
$\log2-1$
$\log4-1$

An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement, then the probability that both drawn balls are black, is

The point on the curve $y^2 = x$ where tangent makes $45^\circ$ angle with $x-$axis is:

Choose the correct answer from the given four options.
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is:

Let $f : R \rightarrow R$ be given by $f(x) = [x^2] + [x + 1] - 3$ where $[x]$ denotes the greatest integer less than or equal to $x.$ Then, $f(x)$ is:

The direction ratios of the normal to the plane 7x + 4y - 2z + 5 = 0 are:

7, 4, -2
7, 4, 5
7, 4, 2
4, -2, 5