As mentioned above, f(x) is standard function notation pronounced eff of ex. Let me provide an example of its usage -

The line below is our "function definition", if you will.

f(x) = 2x + x^{2}

So, f(x) is two x plus x squared. Simple enough. Now we've defined that function, what if we want to put a value into it and work out the answer? We write it like this -

f(2) = (2 * 2) + 2^{2}

f(2) = 4 + 4

f(2) = 8

Function notation is very handy in a lot of math work, especially that involving graphs. See Common graph shifts and stretches.