State with reason whether following functions have inverse h:{2,3,4,5} →{7,9,11,13} with h={(2,7),

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1.Relation and Function

easy

State with reason whether following functions have inverse $h:\{2,3,4,5\} \rightarrow\{7,9,11,13\}$ with $h=\{(2,7),(3,9),(4,11),(5,13)\}$

Option A

Option B

Option C

Option D

Solution

$h :\{2,3,4,5\} \rightarrow\{7,9,11,13\}$ defined as

$h =\{(2,7)\,,(3,9),\,(4,11),\,(5,13)\}$

It is seen that all distinct elements of the set $\{2,3,4,5\}$ have distinct images under $h$.

$\therefore$ Function $h$ is one – one.

Also, $h$ is onto since for every element $y$ of the set $\{7,9,11,13\},$ there exists an element $x$ in the set $\{2,3,4,5\},$ such that $h ( x )= y$.

Thus, $h$ is a one-one and onto function.

Hence, $h$ has an inverse.

Standard 12

Mathematics

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medium

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normal

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medium

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medium

State with reason whether following functions have inverse $h:\{2,3,4,5\} \rightarrow\{7,9,11,13\}$ with $h=\{(2,7),(3,9),(4,11),(5,13)\}$

Solution

Similar Questions

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