for even powers: f(x) = f(-x)

and for odd powers: f(x) = -f(-x)

thus we need only odd powers

but even number of odd powers will result in a positive value, thus we need

**odd number of odd powers**.

(-x)^{3} = -x^3

(-x)^2 = x^2

now just plug in values like -1, 1 or -2, 2 and you’ll get A as the ans

PS:

For option (A),

f(1) = \frac{1^3}{1^2 +1} = \frac{1}{2}

f(-1) = \frac{(-1)^3}{(-1)^2 +1} = \frac{-1}{2}

=> f(1) = f(-1)

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