Question

If the graph of the function $\frac{3^y-1}{\left[\right(y^n\left)\right(3^y+1\left)\right]}$ is symmetric about the y axis then determine the possible value of ‘n.’

• A. 2
• B. 4
• C. 3
• D. 6

Answer 1

The correct option is C 3

$f\left(y\right)=\frac{3^y-1}{\left[\right(y^n\left)\right(3^y+1\left)\right]}=\left[\frac{1}{\left(y^n\right)}\right]\left[\frac{(3^y-1)}{(3^y+1)}\right]=h\left(y\right)g\left(y\right)$

Consider $g\left(y\right)=\frac{(3^y-1)}{(3^y+1)}$

$g(-y)=\frac{(3^{-y}-1)}{3^{-y}+1}=\frac{(1-3^y)}{1+3^y}=-g\left(y\right)$

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)$\times$odd function = even function

$\to$ h(y) should be an odd function

h(y) =$\frac{1}{y^n}$

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

Hence option (c)