Q13 of 215 Page 2

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

Give examples of two functions f: N → N and g: N → N such that gof is onto, but f is not onto.

Give examples of two functions f: N → Z and g: Z → Z such that gof is injective, but g is not injective.

If f: A → B and g: B → C are onto functions show that gof is an onto function.

Find fog and gof, if

f(x) = e^x, g(x) = log_ex