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

Question

, which of the following is even?
I. f(x)
II. f(lxl)
III. lf(x)l
A. I only
B. II only
C. I and II only
D. I and III only
E. None of these

Answer 1

f(x) is not even, because
f(2) = 8
f(-2) = -2

g(x) = f(|x|) is even because
g(-x) = f(|-x|) = f(|x|) = g(x)

|f(x)| is not even because
|f(2)| = |8| = 8
|f(-2)| = |-2| = 2