Did this easily, injective was simple enough, and showed that $\displaystyle f \neq 4$Let $\displaystyle A = \mathbb{R} \backslash \{ 4 \}$

Let $\displaystyle f(a) = \frac{2a + 3}{a-4}$ for all $\displaystyle a \in A$.

Show $\displaystyle f$ is injective but not surjective.

No idea where to start with this, obviously need to show that this new function is now surjective as well as injective, but not sure how to do this seeing as I just proved that an extremely similar function isn't surjective!!For which element $\displaystyle b$ of $\displaystyle \mathbb{R}$ is it true that there's a bijective function $\displaystyle g: A \to \mathbb{R} \backslash \{ b \}$ such that $\displaystyle g(a) = \frac{2a + 3}{a-4}$ for all $\displaystyle a \in A$.

Any help would be greatly appreciated.