State with reason whether following functions have inverse g :{5,6,7,8} →{1,2,3,4} with g={(

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1.Relation and Function

easy

State with reason whether following functions have inverse $g :\{5,6,7,8\} \rightarrow\{1,2,3,4\}$ with $g=\{(5,4),(6,3),(7,4),(8,2)\}$

Option A

Option B

Option C

Option D

Solution

$g :\{5,6,7,8\} \rightarrow\{1,2,3,4\}$ defined as

$g =\{(5,4),(6,3),(7,4),(8,2)\}$

From the given definition of $g$, it is seen that $g$ is a many one function as $g(5)=g(7)=4$

$\therefore g$ is not one – one.

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

Standard 12

Mathematics

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