f(x) = 3x3 + x.
Explanation:
A function is
Condition 1: Even when, f(x) = f(-x)
Condition 2: Odd when, f(x) = -f(-x)
Here, f(x) = 3x3 + x and
f(-x) = 3(-x)3 + (-x) = -3x3 - x
∴ f(-x) = -f(x)
f(x) satisfies the 2nd condition; hence it is an odd function.
[Note: When two odd functions are added / subtracted, the resulting function will also be odd.]
Hence, 2.
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