Soln:

f(y) = (3^y – 1)/[(yⁿ)(3^y + 1)] = [1/(yⁿ)][ (3^y – 1)/(3^y + 1)] = h(y) g(y)

Consider g(y) = (3^y – 1)/(3^y + 1)

g(-y)= (3^-y – 1)/(3^-y + 1)= (1 – 3^y)/(1 + 3^y) = -g(y)

So, g(y) is an odd function.

Now, as f(y) is symmetric about the y axis, f(y) is an even function.

h(y)*odd function = even function

→ h(y) should be an odd function

h(y) = 1/yⁿ

for h(y) to be odd, n has to be odd.

Hence option (c)

 Shortcut

Put y=1 and y=-1, since it is mentioned that it is symmetric about the y axis. The values of both expressions should be equal. This will happen only if n is odd. Hence the answer is option (c)