If the graph of the function `f(x)=(a^x-1)/(x^n(a^x+1))` is symmetric about y-axis, then n equals

Options

A. 2
B. `(2)/(3)`
C. `(4)/(3)`
D. `-(1)/(3)`

Answer

D

Explanation

`f(x)=(a^(x)-1)/(x^(n)(a^(x)+1))`
`f(x)` is symmetrical about y-axis. Thus,
`f(x)=f(-x)`
`or (a^(x)-1)/(x^(n)(a^(x)+1))=(a^(-x)-1)/((-x)^(n)(a^(-x)+1))`
`or (a^(x)-1)/(x^(n)(a^(x)+1))=(1-a^(x))/((-x)^(n)(1+a^(x)))`
`or x^(n)= -(-x)^(n)`
Hence, the value of n which satisfies this relation is ` -(1)/(3)`.