Is the correct notation to represent a function f(x) or simply f?

Either way is fine (once you know what you're doing). However, if you're wanting to specify what is the independent variable for the function, you would include the "of x" part: \((x)\) For instance, in trigonometry, we have the sine function. The name is "sine". But when we are specifying what is going into the sine, we abbreviate and use parentheticals: \(\sin(\theta)\) or \(\sin\left(\frac{\pi}{2}\right)\)