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 is

A. a bijection

B. injective but not surjective

C. surjective but not injective

D. neither injective nor surjective

Answer :

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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