Question

Explain the difference between f and f(x).

Answer 1

\(f\) 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 \(f_2(x)\)