Find the domain of f(x)= ^ -1 (-x^2 ). - Vidyadip

Question

Find the domain of $f(x)=\sin ^{-1}\left(-x^2\right)$.

✓

Answer

The domain of $\sin ^{-1} x$ is $[-1,1]$.
Therefore, $f(x)=\sin ^{-1}\left(-x^2\right)$ is defined for all $x$ satisfying $-1 \leq-x^2 \leq 1$
$ \Rightarrow 1 \geq x^2 \geq-1$
$\Rightarrow 0 \leq x^2 \leq 1$
$\Rightarrow x^2 \leq 1$
$\Rightarrow x^2-1 \leq 0$
$\Rightarrow(x-1)(x+1) \leq 0$
$\Rightarrow-1 \leq x \leq 1 $
Hence, the domain of $f(x)=\sin ^{-1}\left(-x^2\right)$ is $[-1,1]$.

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 2→Model Paper 2 — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate the following:$\big[2\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat{\text{i}}\hat{\text{k}}\hat{\text{j}}\big]+\big[\hat{\text{k}}\hat{\text{j}}2\hat{\text{i}}\big]$

$\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right) =?$

Find the unit vector in the direction of $3\hat{\text{i}}+4\hat{\text{j}}-12\hat{\text{k}}$.

Find the cartesian form of the equation of a plane whose vector equation is:
$\vec{\text{r}}\cdot\big(12\hat{\text{i}}-3\hat{\text{j}}+4\hat{\text{k}}\big)+5=0$

If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=4\text{t, y}=\frac{4}{\text{t}}$

For which value of $k$, square matrix $\left[\begin{array}{cc}k & 8 \\ 4 & 2 k\end{array}\right]$ is non-invertible matrix?

If $f : R \rightarrow R, g : R \rightarrow R$ are given by $f(x) = (x + 1)^2$ and $g(x) = x^2 + 1,$ then write the value of $fog(-3).$

If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find
A + B and B + C

A factory produces bulbs. The probability that one bulb is defective is $\frac{1}{50}$ and they are packed in boxes of 10. From a single box, find the probability that.
exactly two bulbs are defective.

Let $'o\ '$ be a binary operation on the set $Q_0$ of all non$-$zero rational numbers defined by $\text{a}\ ^*\ \text{b}=\frac{\text{ab}}{2} $ for all $\text{a},\text{b}\in\text{Q}_0.$
Find the identity element in $Q_0.$