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|

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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