An even function is when f(x) = f(-x) ... or ... g(x) = g(-x).
f(x) = - (x + 1)(x - 4)
= -(x² - 3x - 4)
= -x² + 3x + 4 f(x) = -x² + 3x + 4
f(-x) = -(-x)² + 3(-x) + 4
= -x² - 3x + 4 f(-x) = -x² - 3x + 4
f(x) ≠ f(-x) so it is NOT even.
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g(x) = [tex]\frac{3}{2}|x|[/tex]
g(-x) = [tex]\frac{3}{2}|-x|[/tex]
= [tex]\frac{3}{2}|x|[/tex] since absolute value becomes positive
g(x) = g(-x) so it IS even
Answer: C
