Let f(x) = |x - 3| + |x - 4| + |x - 5| and g(x) = [f(x)]2. Then
Explanation:
Let us calculate values of f(x) and g(x) for x = 1 and -1.
f(1) = |1 - 3| + |1 - 4| + |1 - 5| = 2 + 3 + 4 = 9
∴ g(1) = 92 = 81
f(-1) = |-1 - 3| + |-1 - 4| + |-1 - 5| = 4 + 5 + 6 = 15
∴ g(1) = 152 = 225
Since f(1) ≠ ± f(-1)
⇒ f(x) is neither even nor odd function
Also. Since g(1) ≠ ± g(-1)
⇒ g(x) is neither even nor odd function
Hence, option (d).
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