Q. 21 C5.0( 2 Votes )

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

h(x) = x |x|

Answer :

Given that, A = [–1, 1]

let h(x_{1}) = h(x_{2})

⇒ x_{1}|x_{1}|= x_{2}|x_{2}|

if x_{1,}x_{2} >0

⇒ x_{1}^{2} = x_{2}^{2}

⇒ x_{1}= x_{2}

if x_{1,}x_{2} < 0

⇒ x_{1}^{2} = x_{2}^{2}

⇒ x_{1}= x_{2}

⇒ h is one-one.

Let h(x) = y

⇒ y = x |x|

⇒ y = x^{2}

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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