Let `G(x)=(1/(a^x-1)+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?`G(x)`is an odd function`G(x)i s`an even function`G(x)`isneither even nor odd function.Whether `G(x)`is an odd or even functiondepends on the value of aA. G(x) is an odd functionB. G(x) is an even functionC. G(x) is neither even function nor odd functionD. Whether G(x) is an odd function or an even function, it depends on the value of a

Let `G(x)=(1/(a^x-1)+1/2)F(x),`where a is a positive real number not e

1.	Let `G(x)=(1/(a^x-1)+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?`G(x)`is an odd function`G(x)i s`an even function`G(x)`isneither even nor odd function.Whether `G(x)`is an odd or even functiondepends on the value of aA. G(x) is an odd functionB. G(x) is an even functionC. G(x) is neither even function nor odd functionD. Whether G(x) is an odd function or an even function, it depends on the value of a
Answer» Correct Answer - B `G(x)=((1)/(a^(x)-1)+(1)/(2))F(x)` `thereforeG(-x)=((1)/(a^(-x)-1)+(1)/(2))F(-x)` `=-((a^(x))/(1-a^(x))+(1)/(2))F(x)` `=((a^(x))/(a^(x)-1)-(1)/(2))F(x)` `=((a^(x)-1+1)/(a^(x)-1)-(1)/(2))F(x)` `=(1+(1)/(a^(x)-1)-(1)/(2))F(x)` `=((1)/(a^(x)-1)+(1)/(2))F(x)=G(x)` `thereforeG(x)` is an even function.