Answer:
(C) g(x) = x² and (E) g(x) = -|x|
Step-by-step explanation:
If f(x) is an even function, then f(-x) = f(x).
(A)
g(x) = 5x + 2
g(-x) = 5(-x) + 2 = -5x + 2
g(-x) ≠ g(x)
(B)
g(x) = g(x) = x
g(-x) = -x
g(-x) ≠ g(x)
(C)
g(x) = x²
g(-x) = (-x)² = (-1x)² = (-1)²(x)² = x²
g(-x) = g(x)
(D)
g(x) = x³
g(-x) = (-x)³ = (-1x)³ = (-1)³(x)³ = -1x³ = -x³
g(-x) ≠ g(x)
(E)
g(x) = -|x|
g(-x) = -|-x| = -|-1x| = -(|-1|)(|x|) = -1|x| = -|x|
g(-x) = g(x)
