Question

Let $G\left(x\right)=\left(\frac{1}{a^x-1}+\frac{1}{2}\right)$ where 'a' is a positive real number not equal to 1 and F(x) is an odd function . Which of the following statement is true

• A. G(x) is an odd number
• B. G/(x) is a even function
• C. G(x) is neither even nor odd
• D. whether g(x) is even or odd it depend on the value of 'a'

Answer 1

The correct option is A G(x) is an odd number

$G\left(x\right)=\frac{1}{a^x-1}+\frac{1}{2}$

$G(-x)=\frac{1}{a^{-x}-1}+\frac{1}{2}=\frac{a^x}{1-a^x}+\frac{1}{2}=-\frac{a^x-1+1}{a^x-1}+\frac{1}{2}=-G\left(x\right)$