If f: a to b and g: b to c be one to one and onto functions then prove that g.f is also one to one and onto
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clearly gof :a to c
g(f(a))=g(f(b))
as g is 1-1 ,f(a)=f(b)
as f is 1-1 ,a=b
so gof is 1-1
for every gof(x)
as g is onto,there is unique f(x)
as f is onto, there is unique x
so gof is onto
g(f(a))=g(f(b))
as g is 1-1 ,f(a)=f(b)
as f is 1-1 ,a=b
so gof is 1-1
for every gof(x)
as g is onto,there is unique f(x)
as f is onto, there is unique x
so gof is onto
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