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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