Assume that alpha:S-T, and beta: T-U, gamma: T-U. prove each of the following statements
A) If alpha and beta are invertible, then beta of alpha is invertible.
I do the first one.
A function is invertible if and only if it is one-to-one.
Say $\displaystyle \beta (\alpha (x) ) = \beta(\alpha(y)) \implies \alpha(x) = \alpha(y) \implies x=y$.
Thus, $\displaystyle \beta \circ \alpha$ is invertible.