Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

h(x) = x |x|

Given that, A = [–1, 1]


let h(x1) = h(x2)


⇒ x1|x1|= x2|x2|


if x1,x2 >0


⇒ x12 = x22


⇒ x1= x2


if x1,x2 < 0


⇒ x12 = x22


⇒ x1= x2


⇒ h is one-one.


Let h(x) = y


⇒ y = x |x|


⇒ y = x2


Thus, for each y co domain there exists x in domain.


⇒ h is onto.


Hence, h is one one and onto.


So, h is bijective.


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