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Q. 3 State with reason whether following functions have inverse

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

Answers (1)

S seema garhwal

(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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