f(x) is a way of writing the output of a function, also known as the dependent variable. You are probably used to seeing y in this place, but all you're doing is replacing y with f(x).
[tex]3x+4y=10 \\ 4y=-3x+10 \\ y = \frac{-3}{4}x+ \frac{5}{2} \\ \\ f(x) = \frac{-3}{4}x+ \frac{5}{2} [/tex]
