Show that the function f : R R given by f(x) = x 3 is injective.

Let x 1 , x 2 R be such that, f( x 1 ) = f( x 2 ) x 1 3 = x 2 3 = x 2 f is one - one. Hence, f(x) = x 3 is injective.

Relations and Functions — Class 12 Maths Solution

ncert misc SA NCERT Misc.,Q.5, Page 29

Question

Show that the function f : R $\rightarrow$ R given by f(x) $= x^3$ is injective.

Step-by-step Solution

Let ${x_1},{x_2} \in R$ be such that,

$f({x_1}) = f({x_2}) \Rightarrow x_1^3 = x_2^3 \Rightarrow {x_1} = {x_2}$

$\therefore$ f is one$-$one. Hence, f(x) $= x^3$ is injective.

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Relations and Functions. Curated by Sachin Sharma. Free for all students.