Confusing Surjective Question

Quote:

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.

Did this easily, injective was simple enough, and showed that $\displaystyle f \neq 4$

Quote:

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 $\displaystyle a \in A$.

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!!

Any help would be greatly appreciated.