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

Q. 3 State with reason whether following functions have inverse

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

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

From the definition, we can see the set $\left \{ 2,3,4,5 \right \}$ have distant values under h.

$\therefore$ h is one-one .

For every element y of set $\left \{ 7,9,11,13 \right \}$,there exists an element x  in $\left \{ 2,3,4,5 \right \}$ such that  $h(x)=y$

$\therefore$ h is onto

Thus, h is one-one and onto so h has an inverse function.

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