State with reason whether following functions have inverse f: {1,2,3,4}→{10} with f ={(1,10),(2,10

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1.Relation and Function

easy

State with reason whether following functions have inverse $f: \{1,2,3,4\}\rightarrow\{10\}$ with $f =\{(1,10),(2,10),(3,10),(4,10)\}$

Option A

Option B

Option C

Option D

Solution

$f :\{1,2,3,4\} \rightarrow\{10\}$ defined as $f =\{(1,10),(2,10),(3,10),(4,10)\}$

From the given definition of $f$, we can see that $f$ is a many one function as

$f(1)=f(2)=f(3)=f(4)=10$

$\therefore f$ is not one – one.

Hence, function $f$ does not have an inverse.

Standard 12

Mathematics

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