A set of all possible values the function f(x) = x|x|, where x ≠ 0, takes is
Explanation:
Given, f(x) = x|x|
Case 1: x > 0 ⇒ |x| = x ∴ f(x) = xx = 1
Case 2: x < 0 ⇒ |x| = - x ∴ f(x) = x-x = - 1
∴ f(x) = 1 when x > 0 while f(x) = -1 when x < 0.
⇒ f(x) can take only two values {1, -1}.
Hence, option (b).
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