A Letter as Input

The input does not have to be a number. Any expression can go in, and the rule treats it exactly as it treats a number: it replaces every x with the whole input. For g(x) = 4x + 1, the input 3a gives g(3a) = 4(3a) + 1.

Then you tidy up as usual. 4(3a) is 12a, so g(3a) = 12a + 1. Here the answer is an expression, because the letter a survives the arithmetic. It does not have to: a rule that ignores its input, like k(x) = 5, gives 5 whatever goes in.

This is how functions talk about many inputs at once. Knowing g(3a) for every a tells you g(3), g(6), g(9) and the rest in a single line.