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

Question

Philoid · Accepted Answer

Given that, A = [–1, 1]

Let f(x₁) = f(x₂)

⇒

⇒ 2x₁ = 2x₂

⇒ x₁ = x₂

⇒ f is one one

Now, let f(x) = y

⇒

⇒ 2y= x

⇒ for y=1 ∈ A we will have x = 2 ∉ A

⇒ f is not onto

Thus, f is one-one and not onto.