If the real valued function $f(x)=\frac{

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

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

Options:

2/3

1/4

1/3

Correct Answer:

1/3

Explanation:

$f(x)=\frac{a^x-1}{x^n\left(a^x+1\right)}$

$f(x)$ → even

$⇒f(-x)=f(x)$

so $f(-x)=\frac{a^{-x}-1}{(-x)^n(a^{-x}+1)}=\frac{1-a^x}{(-x)^n(1+a^x)}$

so $f(-x)=-1×(-x)^n×\frac{a^x-1}{a^x+1}$

$⇒-(-x)^n=(x)^n$

$⇒n=1/3$