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

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G(x) is an odd function

G(x) is an even function

G(x) is neither even function nor odd function

Whether G(x) is an odd function or an even function, it depends on the value of a

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detailed solution

Correct option is B

G(x)=1ax−1+12F(x)∴ G(−x)=1a−x−1+12F(−x) =−ax1−ax+12F(x) =axax−1−12F(x) =ax−1+1ax−1−12F(x) =1+1ax−1−12F(x)=1ax−1+12F(x)=G(x)∴G(x) is an even function.

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Let G(x)=1ax−1+12F(x), where a is a positive real number not equal to 1 and F(x) is an odd function. Which of the following statements is true?

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