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?

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.