Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Choose the correct answer from the given four options.The domain of the function defined by $\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$ is:
  • ✓
    $[1, 2]$
  • B
    $[-1, 1]$
  • C
    $[0, 1]$
  • D
    none of these.
✓

Answer

Correct option: A.
$[1, 2]$
$\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$
$\Rightarrow\ 0\leq\text{x}-1\leq1\ [\because\ \sqrt{\text{x}-1}\geq0$ and $-1\leq\sqrt{\text{x}-1}\leq1]$
$\Rightarrow\ 1\leq\text{x}\leq2$
$\therefore\ \text{x}\in[1,2]$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $y(x)=x^2, x > 0$, then $y^{\prime \prime}(2)-2 y^{\prime}(2)$ is equal to :
→
Find the intervals in which the function $f$ given by $f(x)=x^2-4 x+6$ is strictly increasing.
→
If $A = \left\{ {1,2,3,......m} \right\},$ then total number of reflexive relations that can be defined from $A \to A$ is 
→
$\int {\,\,\frac{{{x^2}\,\, + \,\,{{\cos }^2}\,x}}{{1\,\, + \,\,{x^2}}}}$ $cosec^2\, x\, dx$ is equal to :

where $‘c’$ is constant of integration .

→
Value of $\left| {\begin{array}{*{20}{c}}
  {{{(b + c)}^2}}&{{a^2}}&{{a^2}} \\ 
  {{b^2}}&{{{(a + c)}^2}}&{{b^2}} \\ 
  {{c^2}}&{{c^2}}&{{{(a + b)}^2}} 
\end{array}} \right|$ is equal to
→
If a line makes $45^\circ , 60^\circ$ with positive direction of axes $x$ and $y$ then the angles it makes with the $z-$axis is:
→
If the fucnction $\text{f(x)}=\begin{cases}(\cos\text{x})^{\frac{1}{\text{x}}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuouse at x = 0, then the value of k is:
→
Let $f$ be a differentiable function such that $f(1) = 2$ and $f\,'(x) = f(x)$ for all $x\in R.$ If $h(x) = f(f(x)),$ then $h'(1)$ is equal to
→
Let $f : R \rightarrow R$ be a function defined by $f ( x )=$ $\log _{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}$, for some $m$, such that the range of $f$ is $[0,2]$. Then the value of $m$ is $............$
→
The area of the region (in sq. units), in the first quadrant bounded by the parabola $y = 9x^2$ and the lines $x = 0,y = 1$ and $y = 4,$ is
→