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Question: Which of the following functions is neither even nor odd?
A ) f (x) = (x - 2)2
B ) h (x) = |x| - 2
C ) g (x) = x2 + 4
D ) k (x) = x3
Steps to derive
1 For the choice A:
f (- x) = (- x - 2)2 = (x + 2)2 ≠ ± f (x)
2 Since f (- x) ≠ f (x) or f (- x) ≠ - f (x), the given function is neither even nor odd.
3 For the choice B:
k (- x) = |- x| - 2 = |x| - 2 = k (x)
4 Hence, it is an even function.
5 For the choice C:
g (- x) = (- x)2 + 4 = x2 + 4 = g (x)
6 Hence, it is an even function.
7 For the choice D:
h (- x) = (- x)3 = - x3 = - h (x)
8 Hence, it is an odd function.
Hence the right answer is Option A
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