5
$\begingroup$

Suppose $f(x) = g(x) + h(x)$ where $g(x)$ is known to be non-differentiable. When $h(x) \ne -g(x)$ is some other function (differentiable or not), can $f(x)$ ever be differentiable? We can assume $f, g, h$ are real valued functions.

edit: I should have specified that $h(x)$ is not some function that cancels out $g(x)$ . Bill Dubuque's answer is intriguing.

  • 1
    What does "some function that cancels out $g(x)$" mean?2011-05-02
  • 2
    The difficulty is that there is no rigorous notion of what it means to say "$h(x)$ is not some function that cancels out $g(x)$". **Any $h(x)$** is a function that "cancels out $g(x)$", because we have that $h(x)=f(x)-g(x)$.2011-05-02

4 Answers 4