Every relation is a function.

Important Questions on Relations and Functions

MEDIUM

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 2

The number of bijective functions from a set $A$ onto itself is $n^n$ when $\left|A\right|=n$.

MEDIUM

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 2

If $f:A\to B$ and $X\subseteq A$, then $f^{-1}\left(f\right(X\left)\right)=X$

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 2

Every function is a relation.

MEDIUM

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 2

If $f:A\to B$ is a bijective map and $g:B\to A$ is the inverse of $f$, then $g\circ f=f\circ g=$identity function.

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 2

If $f:A\to B$ and $Y\subseteq B$, then $f\left(f^{-1}\left(Y\right)\right)=Y$

MEDIUM

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

Let $f=\left\{\right(1,p),(2,q),(3,s),(4,x\left)\right\}$ be a relation from the set $A=\{1,2,3,4\}$ into the set $B=\left\{p,q,r,s,t\right\}$. Then the value of $x$(from $B$ ) for which $f$ turns out to be an injective function from $A$ into $B$ is

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

A function $f:A\to B$ is invertible if and only if $f$ is

HARD

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 3

A function $f:A\to B$ is right invertible if and only if $f$ is