Examine whether the function f : R → R is one-one (injective) if f(x

1.	Examine whether the function f : R → R is one-one (injective) if f(x) = x3, x ∈ R.
Answer» Given, the function f : R → R is defined as f(x) = x³, x ∈ R Let x₁, x₂∈ R f(x₁) = f(x₂) x³₁ = x³₂ x₁= x₂ Thus the given function is one-one or injective.

Examine whether the function f : R → R is one-one (injective) if f(x) = x3, x ∈ R.

Answer»

Given, the function f : R → R is defined as f(x) = x³, x ∈ R

Let x₁, x₂∈ R

f(x₁) = f(x₂)

x³₁ = x³₂

x₁= x₂

Thus the given function is one-one or injective.

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Examine whether the function f : R → R is one-one (injective) if f(x) = x3, x ∈ R.

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