Q. 134.8( 6 Votes )

If f: A B and g: B C are one – one functions show that gof is a one – one function.

Answer :

We have, f : A B and g : B C are one – one functions.


Now we have to prove : gof: A C in one – one


let x, y A such that


gof(x) = gof(y)


g(f(x))=g(f(y))


f (x) = f (y) [As, g in one – one]


x = y [As, f in one – one]


gof is one – one function


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