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What is the difference between:

$(f + g)(x)$

and

$f(x) + g(x)$
?

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2  
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

1 Answer 1

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 $f+g$.

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