If the graph of the function is symmetric about the y axis then determine the possible value of ‘n.’

Options:

A . 2

B . 4

C . 3

D . 8

E . 6

Answer: Option C : C Soln: f(y) = (3^{y} – 1)/[(y^{n})(3^{y} + 1)] = [1/(y^{n})][ (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/y^{n} 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)

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