Properties of Functions Question

Does f(x + h) = f(x) + f(h)?

Sometimes, but not always. For example, that statement is true for f(x) = x, since for any a, b f(a+b)=a+b=f(a)+f(b).

However, the statement is false for f(x) = x^2. Consider f(3+4)=f(7)=49, but f(3)+f(4)=25.

So the statement is sometimes true.

@Inorganic: this problem is about linearity properties of functions, not function composition!

The additive property of function composition says that this is true. both f(x) and f(h) share a domain that is with and contains the composite function f(x +h)