If the real valued function f(x)=a^x-1 x^x (a^x+1 ) is even, then… - Vidyadip

MCQ

If the real valued function $f(x)=\frac{a^x-1}{x^x\left(a^x+1\right)}$ is even, then n equals

A
2
B
$\frac{-2}{3}$
C
$\frac{1}{4}$
✓
$-\frac{1}{3}$

✓

Answer

Correct option: D.

$-\frac{1}{3}$

(D)
Since $f (x)$ is even, $f (-x)= f (x)$
$\therefore \quad \frac{ a ^{-x}-1}{(-x)^{ n }\left( a ^{-x}+1\right)}=\frac{ a ^x-1}{x^{ n }\left( a ^x+1\right)}$
$\Rightarrow \frac{1- a ^x}{(-1)^{ n } x^{ n }\left(1+ a ^x\right)}=\frac{ a ^x-1}{x^{ n }\left( a ^x+1\right)}$
$\Rightarrow \frac{-1}{(-1)^{ n }}=1 \Rightarrow-1=(-1)^{ n }$
$\therefore \quad n =-\frac{1}{3}$ can satisfy the equation.

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

The opposite vertices of a square are (1, 2) and (3, 8), then the equation of a diagonal of the square passing through the point (1, 2), is

156° is equal to

If $\sin (\theta-\alpha), \sin \theta$ and $\sin (\theta+\alpha)$ are in H.P., then the value of $\cos 2 \theta$ is

If at the end of certain meeting, everyone had shaken hands with every one else, it was found that 45 handshakes were exchanged, then the number of members present at the meeting are

The probabilities of a student getting first class or second class or third class in an examination are $\frac{2}{7}, \frac{3}{5}, \frac{1}{10}$ respectively. The probability that the student fails is

The distance between the directrices of a rectangular hyperbola is 10 units, then distance hetween its foci is

Let $z_1=3+4 i$ and $z_2=-1+2 i$. Then $\left|z_1+z_2\right|^2-2\left(\left|z_1\right|^2+\left|z_2\right|^2\right)$ is equal to

If the latus rectum of an hyperbola be 8 and eccentricity be $\frac{3}{\sqrt{5}}$, then the equation of the hyperbola is

Let $R$ be a relation on $N$ defined by $x + 2y = 8$. The domain of $R$ is :

The equation $5 x^2+y^2+y=8$ represents