forf◦g. In the same way we findg◦f:12345↓↓↓↓↓24422h◦g:12345↓↓↓↓↓42244h◦h:12345↓↓↓↓↓12345Note thath◦his the identity map.(b)We findh◦(g◦f) :12345↓↓↓↓↓42244and(h◦g)◦f:12345↓↓↓↓↓42244These are the same, which is consistent with theassociativity of composition, which assertsthath◦(g◦f) = (h◦g)◦f.(c)Onlyfandhare one to one, onto and invertible, whilegis none of these things.We have seen above thath◦his the identity map, soh-1=h. To findf-1, just run itbackwards: sincef(5) = 1,f-1(1) = 5. sincef(1) = 2,f-1(2) = 1, and so on, with theresult thatf-1:12345↓↓↓↓↓513241.5Consider the function from
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