# Prove (f+g)(x) = f(x) + g(x)

where f and g are finctions of x

you mean "functions"...

that's a definition as far as I am concerned. How are you defining (f+g)(x)?

This appears to be the definition of the sum of two functions. It is valid as long as f and g have the same domains and ranges.

JasonRox
Homework Helper
Gold Member
This appears to be the definition of the sum of two functions. It is valid as long as f and g have the same domains and ranges.
They don't need the same range.

Try sin(x) + x.