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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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