12th Class Mathematics Relations and Functions Question Bank Case Based (MCQs) - Relations and Functions

Let \[f:\left\{ 1,\,2,\,3\,.... \right\}\to \left\{ 1,\,4,\,9,\,... \right\}\]be defined by \[f\left( x \right)={{x}^{2}}\]is

A) Bijective

B) Surjective but not Injective

C) Injective but Surjective

D) Neither Surjective nor Injective.

Correct Answer: A

Solution :

\[A=\left\{ 1,\,\,2,\,\,3,\,\,... \right\}\]

\[B=\left\{ 1,\,\,4,\,\,9,\,\,... \right\}\]

\[x=1,\,\,y=1\]

\[x=2,\,\,y=4\]

\[x=3,\,\,y=9\]

So on

\[\therefore \,f\left( x \right)\] is one - one onto

\[\Rightarrow \,\,\,f\left( x \right)\] is Bijective function.