Download App

Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The function $f(x)=\sin \left(\log \left(x+\sqrt{\left.x^2+1\right)}\right)\right.$ is
  • A
    Even function
  • ✓
    Odd function
  • C
    Neither even nor odd
  • D
    peridic function
✓

Answer

Correct option: B.
Odd function
(B)
$f (x)=\sin \left(\log \left(x+\sqrt{1+x^2}\right)\right)$
$\rightarrow f (-x)=\sin \left[\log \left(-x+\sqrt{1+x^2}\right)\right]$
$\Rightarrow f (-x)=\sin \log \left(\left(\sqrt{1+x^2}-x\right) \frac{\left(\sqrt{1+x^2}+x\right)}{\left(\sqrt{1+x^2}+x\right)}\right)$
$\Rightarrow f (-x)=\sin \log \left[\frac{1}{x+\sqrt{1+x^2}}\right]$
$\Rightarrow f (-x)=\sin \left[-\log \left(x+\sqrt{1+x^2}\right)\right]$
$\Rightarrow f (-x)=-\sin \left[\log \left(x+\sqrt{1+x^2}\right)\right]$
$\Rightarrow f (-x)=- f (x)$
$\therefore f (x)$ is odd function.

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 "MCQ" from Functions→Functions — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\alpha,\beta$ are the roots of the equation $x^2− p(x + 1) − c = 0$, then $(\alpha+1)(\beta+1)=$
→
There are $12$ points in a plane. The number of the straight lines joining any two of them when $3$ of them are collinear is :
→
If $A$ and $B$ are two sets such that $\text{n(A)}=70, \text{ n(B)}=60, \text{ n(A}\cup\text{B)}=110,$ then $\text{n(A}\cap\text{B)}$ is equal to :
→
If $x+ i y=\frac{3}{2+\cos \theta+ i \sin \theta}$, then $x^2+y^2$ is equal to
→
If $a \tan \theta= b$, then $a \cos 2 \theta+ b \sin 2 \theta=$
→
In shuffling a pack of playing cards, four cards are accidently dropped. The probabillity that the missing cards should be one from each suit is
→
If $f (x)=\frac{2-\sqrt{x+4}}{\sin 2 x} ;(x \neq 0)$, is continuous function at $x=0$, then $f(0)$ equals
→
$f(x)=\left\{\begin{array}{cl}2 x+1, & x<1 \\ 2, & x=1 \ is\\ x^2+1, & x>1\end{array}\right.$
→
If $a, b, c$ are in $G.P$. is $2$ and $x, y$ are $AM\ '$s between $a, b$ and $b, c$ respectively, then :
→
If $f(x)=\left\{\begin{array}{ll}k x^2 & \text { if } x \leq 2 \\ 3 & \text { if } x>2\end{array}\right.$ is continuous at $x=2,$ then the value of $k$ is
→