Show that function f: R → R be defined by f (x) = x³ is injective

Solution:

In mathematics, an injective function ( or one-to-one function) is a function f such that maps distinct elements to distinct elements

that is, f(x₁) = f (x₂) 

⇒ x₁ = x₂

f : R → R be defined by

f (x) = x³

For one-one:

f (x) = f (y) where x, y ∈ R

x³ = y³ .... (1)

We need to show that x = y

Suppose x is not equal to y, their cubes will also not be equal.

⇒ x³ ≠ y³

This will be a contradiction to (1).

Therefore,

x = y.

Hence, f is injective

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise ME Question 5

Show that function f: R → R be defined by f (x) = x³ is injective

Summary:

Here we have concluded that function f: R → R be defined by f (x) = x³ is injective