functions theorems inter 1st year in telugu|Functions theorem-1|functions theorems in telugu

functions theorems inter 1st year in telugu|Functions theorem-1|functions theorems in telugu
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f from AtoB and g from to BtoC be a bijcetion then gof from AtoC is a bijection
inter 1st year maths 1a functions theorem 1
Theorem-1:
f from A to B,g from B to C be bijectionsThen show that gof from A to C is a bijection
Theorem-2:
Let f from A to B,g from B to C be bijectionsThen show that (gof) ^ - 1 =f^ -1 og^ -1
Theorem-3:
Let f from A to B be a bijectionThen show that fof^-1=IB and f ^ - 1 of = IA
Theorem-4:
Let f from A to B, IA and IB be Identity functions on Aand B respectively. Then showthr folA=f=IB
Theorem-5:
Let f from A to B be a bijection. Then show that f is a bijection if and only if there exists a function g from B to A such that fog=IBand gof=IA and in this case, g=f^-1

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