When to use `\left(` and when plain `(`? [duplicate]

Question

This is basically a follow-up to the comments on this answer which I couldn't find to be settled anywhere. I learned that you can write ordinary bracket simply using

f(x)

but that you can also use

f \left( x \right)

where the latter automatically adopts the brackets' size, but creates a space between the function and the bracket.

My question is: when is one supposed to use which version. Is the second version only used when the "content" of the bracket is not an argument of some function? What if it is a long and complex argument, where I want the brackets to be increasing in size? Would I then use

f \! \left( long expression \right)

or is there some other solution for this?

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Edit: While I found some solutions regarding the space adjustment, I was still wondering when to use which approach, i.e. whether there are some "best practice rules" for this.

Answer 1

1. Use \left only when the largest default delimiter \Biggl is too small. The reason is that IMHO, \left rarely uses the correct size. Moreover, it introduces a spurious thin space around the delimiters; this can be solved using \mleft...\mright from \usepackage{mleftright}.

2. As for f(sin(x)+cos(x)), the correct form is of course f(\sin x+\cos x) :) but suppose you mean f(g(x)+h(x)). Then the usage of larger parentheses is not a clear thing and two good typographers might do it in two different ways. I use the following way:

   • Inline, never use anything larger than \big, so this would be f\bigl( g(x)+h(x) \bigr), but likely \bigl\{ f\bigl(g(x)+h(x)\bigr) \bigr\} _ {x\in[0,1]}.

   • On display, I generally increase the size with every nested pair, unless it becomes too big.

3. Fractions, sums, integrals: I personally do not mind things "sticking out" a bit of the delimiters. Hence I would use the following

   • Inline: $ \bigl(\frac{1}{4}\bigr) = \bigl( \int_0^{1/2} dx \bigr)^{1/2} = \bigl( \sum_{i=2}^\infty 2^{-i} \bigr)^{1/2} $

   • On display: \[ \Bigl(\frac{1}{4}\Bigr) = \biggl( \int_0^{1/2} dx \biggr)^{1/2} = \biggl( \sum_{i=2}^\infty 2^{-i} \biggr)^{1/2} \]

4. Use \begin{pmatrix} and similar for column vectors and matrices (requires \usepackage{amsmath})