Can somebody prove that the composition of two one-to-one functions is also a one-to-one function?

Question

Can somebody prove that the composition of two one-to-one functions is also a one-to-one function?

Answer 1

Sure. What part of the proof are you having trouble with? Do you understand one one-to-one means?

http://en.wikipedia.org/wiki/One-to-one

Suppose H(x) = G(F(x))

if F and G are one to one, then for all x and y, if x is not y, then F(x) is not F(y). If F(x) is not F(y), then G(F(x)) can't be G(F(y)). Therefore H(x) is not H(y).