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 x_1,x₂ >0

⇒ x₁² = x₂²

⇒ x₁= x₂

if x_1,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.