Q. 165.0( 1 Vote )

# Mark the correct alternative in each of the following:Let A = {x : –1 ≤ x ≤ 1} and f : A → A such that f(x) = x |x|, then f isA. a bijectionB. injective but not surjectiveC. surjective but not injectiveD. neither injective nor surjective

Given that A = {x: –1 ≤ x ≤ 1} and f: A A such that f(x) = x |x|.

For x <0, f(x) <0

y = -x2

x = √-y, which is not possible for x > 0.

Hence, f is one-one and onto.

the given function is bijective.

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