Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

What is the difference between:

$(f + g)(x)$


$f(x) + g(x)$

share|cite|improve this question
Nothing, really. $(f+g)$ is just shorthand for the function that is the sum of $f$ and $g$ (unless you had a different meaning of $+$ in mind). – J. M. Apr 27 '11 at 11:10
Right. Thanks J.M. – Joe Apr 27 '11 at 11:18
up vote 8 down vote accepted

$(f+g)(x)$ is the function $f+g$ applied to the argument $x$.

$f(x)+g(x)$ is the sum of the two images of $x$ using $f$ and $g$.

That these two expressions always give the same result is the definition of $f+g$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.