Consider the function g(f(x)) where f: A -- B and g: B -- C. I know that if both f and g are bijective, then g(f(x)) is also bijective and therefore has an inverse. But what if only f is bijective? or if only g is bijective? What does that imply about g(f(x)) ?

Question

Consider the function g(f(x)) where f: A --> B and g: B --> C. I know that if both f and g are bijective, then g(f(x)) is also bijective and therefore has an inverse. But what if only f is bijective? or if only g is bijective? What does that imply about g(f(x)) ?

zzr0ck3r · Answer

Did I not answer this already?

zzr0ck3r · Answer

$f(x)=x$ is a bijection

$g(x)=x^2$ is not a bijection

$f(g(x))=g(f(x))= x^2$ is not a bijection