Let f A B and g B C If g f as a function from A to C is bi

Let f : A B and g : B C. If g f, as a function from A to C, is bijective, then f is injective and g is surjective, but f need not be surjective, nor g need be injective.

The function is said to bijective if it is both one-one and onto, i.e. injective implies one-one and surjective implies onto

The function gof will be one-one if the function f is one-one, since gof is g(f(x)), if the function f is not injective then there may be two values x1 and x2 such that

g(f(x1) = g(f(x2))

Hence the function f must be injective

The final function value depends on the g(f(x)), so if the function g is not surjective then all the range will not be mapped, hence the function g must be surjective

If g is not injective, then it doesn\'t matter, since the function f is injective then g(f(x)) will always be unique mapping

Let f : A B and g : B C. If g f, as a function from A to C, is bijective, then f is injective and g is surjective, but f need not be surjective, nor g need be i

Let f A B and g B C If g f as a function from A to C is bi

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