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