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If the real valued function $f(x)=\frac{a^x-1}{x^n\left(a^x+1\right)}$ is even then n equals |
2 2/3 1/4 1/3 |
1/3 |
$f(x)=\frac{a^x-1}{x^n\left(a^x+1\right)}$ $f(x)$ → 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 $f(-x)=-1×(-x)^n×\frac{a^x-1}{a^x+1}$ $⇒-(-x)^n=(x)^n$ $⇒n=1/3$ |
