Which of the following functions f defined for all numbers has the property f(-x)=-f(x)

GRE Quant Problem Solving
1

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Looking for an example of how to solve this by choosing numbers.

2

Let, x=1

Option A:

f(-x)=\dfrac{x^3}{x^2+1} = \dfrac{(-1)^3}{(-1)^2+1}=\dfrac{-1}{1+1}=-\dfrac{1}{2}\\ -f(x)=-\left(\dfrac{x^3}{x^2+1} \right)= -\left(\dfrac{(1)^3}{(1)^2+1}\right)=-\left(\dfrac{1}{1+1}\right)=-\dfrac{1}{2}

Hence, f(-x) = f(x) for this case! You can do the same and check for other options!

3

Thanks for the help. Is it fair to rule out BCDE because 0 is not equal to -0? Or would choosing a number like 2 be required to confirm this answer?

4

But it is?