Question

Please help 20 POINTS. Problem below

Answer 1

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) =
`(3)/(2)|x|`

g(-x) =
`(3)/(2)|-x|`

=
`(3)/(2)|x|` since absolute value becomes positive

g(x) = g(-x) so it IS even

Answer: C