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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Class 12th RD Sharma - Volume 1 2. Functions

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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