Find the domain of the following function:f(x)= ^ -1 x^2-1 - Vidyadip

Question

Find the domain of the following function:$\text{f(x)}=\sin^{-1}\sqrt{\text{x}^2-1}$

✓

Answer

To the domain of $\sin^{-1}y$ which is $[-1, 1]$
$\therefore x^2 -1 \in [0, 1]$ as square root can not be negative
$\Rightarrow x^2\in [1, 2]$
$\Rightarrow\text{x}\in\big[-\sqrt2,-1\big]\cup\big[1,\sqrt2\big]$
Hence, the domain is $\big[-\sqrt2,-1\big]\cup\big[1,\sqrt2\big]$

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 INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $f : R → $R be defined by $f(x) = x^4$, write $f^{-1}(1).$

For what value of $\lambda$ are the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ perpendicular to each other if
$\vec{\text{a}}=\lambda\hat{\text{i}}+3\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$

If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are non-coplanar vectors, prove that the given vectors are non-coplanar:
$\vec{\text{a}}+2\vec{\text{b}}+3\vec{\text{c}},\ 2\vec{\text{a}}+\vec{\text{b}}+3\vec{\text{c}}$ and $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer:
$f: R → R$ defined by $f(x) = 3 – 4x$

If $\mathrm{A}=\left[\begin{array}{lll}2 & -4 & 3\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{r}2 \\ -4 \\ 8\end{array}\right]$ then find $(\mathrm{AB})^{\mathrm{T}}$.

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

If a line makes angles 90º, 135º, 45º with the x, y and z-axes respectively, find its direction cosines.

A die is thrown 6 times. If “getting an odd number” is a “success”, what is the probability of:

5 successes?
Atmost 5 successes?

Find the area bounded by parabola $x^2=y$ and a straight line $y=x+2$ and $x$-axis.

For the principal values, evaluate the following:
$\sec^{-1}\big(\sqrt2\big)+2\text{cosec}^{-1}\big(-\sqrt2\big)$