If A={1,2,3},B={α,β,λ}C={p,q,r} and f:A→B,g:B→C are defined by f={(1,α),(2,λ)(3,β)} and g={(α,q),(β,r),(λ,p)} Show that f and g are bijective functions and (gof)−1=f−1og−1
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Solution
A={1,2,3},B={α.β},C={p,q,r}
Refer to Image 01
f=A⟶B
f={(1,α),(2,λ),(3,β)}
g=B⟶C
f:A⟶B is clearly a bijective function.
As every element in A has unique image in B and every element of B ∃ unique preimage in A.