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