Find a and b

[nycmathguy]

 

[MathLover1]

If a = 0 and b = 1, we have f(x) = x^3, which is symmetric about the origin. It's easy to show that f(-x) = -f(x) for all x.
If a = 1 and b = 0, we have f(x) = x^2, which is symmetric about the y-axis. It's easy to show that f(-x) = f(x) for all x.

 

[nycmathguy]

If a = 0 and b = 1, we have f(x) = x^3, which is symmetric about the origin. It's easy to show that f(-x) = -f(x) for all x.
If a = 1 and b = 0, we have f(x) = x^2, which is symmetric about the y-axis. It's easy to show that f(-x) = f(x) for all x.

There are many correct answers. Why?