# Show that function f: R → R be defined by f (x) = x^{3} 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(*x*_{1}) = f (*x*_{2})

⇒ *x*_{1} = *x*_{2}

f : R → R be defined by

f (x) = x^{3}

For one-one:

f (x) = f (y) where x, y ∈ R

x^{3} = y^{3} .... (1)

We need to show that x = y

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

⇒ x^{3} ≠ y^{3}

This will be a contradiction to (1).

Therefore,

x = y.

Hence, f is injective

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

## Show that function f: R → R be defined by f (x) = x^{3} is injective

**Summary:**

Here we have concluded that function f: R → R be defined by f (x) = x^{3} is injective