I want to obtain an increase in the size of nested parenthesis with a single command like \left and \right, something like the right term of

but using the code used for the left term.
(The image is created using \left(1 + \left(f(x),g(x)\right)\right) and \Big(1 + \big(f(x),g(x)\big)\Big))
I could simply use \bib, \Big, ... but I don't want to keep track of the content all the time.
I have no clue how to define a new set of \left and \right for this purpose.
\bigl(and\bigr)for the outer parentheses. Size\Bigis definitely excessive. – egreg Jul 15 '20 at 12:19\leftand\right, I can't use\bigland\bigrif the content has a\fracfor example, I want to respect that but always getting a but larger parenthesis that the one the normal\leftwould give. – Jorge E. Cardona Jul 15 '20 at 13:04\delimiterfactor=1001is enough to obtain my desired effect, I will play with the other quantities to see what else do I get. Thanks! – Jorge E. Cardona Jul 15 '20 at 13:14