- #1

- 838

- 37

## Main Question or Discussion Point

If I have a sum ##f(x) + g(x) = c##, with ##c## a constant, does this imply that both ##f(x)## and ##g(x)## are also constants?

If I just solve this equation for ##x##, I will find some values of ##x## which satisfy the equation. However, if I require that the equation be true for all ##x##, there is no way other than the functions being equal to constants. Am I right?

If I just solve this equation for ##x##, I will find some values of ##x## which satisfy the equation. However, if I require that the equation be true for all ##x##, there is no way other than the functions being equal to constants. Am I right?