Question

Explain the difference between f and f(x)

Answer 1

f could just be a variable, or a constant.
whereas f(x) is a function of 'x'
and we call x as an independent variable.

if f is a function, it doesn't mention the independent variable in it, so that variable could be anything

Answer 2

think of f(x) as this
you have something like
f(x) = x + 3
so for this function you would input values of x to get f(x)
for example
f(3) would be
f(3) = 3+3
= 6