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Given that
f(x)= x^3 i f x≥0
x i f x<0

which of the following functions is even?

I. f(x)
II. f(|x|)
III. |f(x)|

  • Calculus -

    f(x) is not even, since

    f(-x) ≠ f(x) for x≠0,1

    f(3) = 27
    f(-3) = -3
    f(|x|) is even since |x| is always positive
    |f(x)| is not even, again, because x ≠ x^3 for x≠0,1

    |f(3)| = 27
    |f(-3)| = 3

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