Explain the difference between f and f(x).

Question

kirbykirby · Answer

$f$ is a function. It takes inputs and then produces an output.
The notation $f(x)$ is saying more specifically that the function is taking an input $x$ and producing the output $f(x)$. 
For example, if you look at $f(x)=x^2$, you can think that $f$ is the "squaring function", with input $x$ and outputs $x^2$. 

You can think that $"f"$ is like the name of the function. 
$f_1(x) = x^2$
$f_2(x) = 6^x+3$

Above, you know which function I'm talking about if I say $f_2$. But often, people will just call it as the function $f_2(x)$