- #1
HappyN
- 16
- 0
The question states:
Give two different examples of f:R->R such that f is continuous and satisfies f(x+y)=f(x)+f(y) for every x,y e R. Find all continuous functions f:R->R having this property. Justify your answer with a proof.
I came up with one example:
f(x)=ax
then f(x+y)=a(x+y)=ax+ay=f(x)+f(y)
however, I can't seem to think of another example, any hints?
Give two different examples of f:R->R such that f is continuous and satisfies f(x+y)=f(x)+f(y) for every x,y e R. Find all continuous functions f:R->R having this property. Justify your answer with a proof.
I came up with one example:
f(x)=ax
then f(x+y)=a(x+y)=ax+ay=f(x)+f(y)
however, I can't seem to think of another example, any hints?