(1) (2007 - National I) $f(x)$ and $g(x)$ are functions defined on $\mathbf{R}$, $h(x) = f(x) + g(x)$, then “$f(x)$ and $g(x)$ are both even functions” is “$h(x)$ is an even function” ( ).
(A) Sufficient and necessary condition
(B) Sufficient but not necessary condition
(C) Necessary but not sufficient condition
(D) Neither sufficient nor necessary condition
Prove sufficiency: From the given, $h(-x)=f(-x)+g(-x)$, then $h(-x)=h(x)$, the function $h(x)$ is an even function.

Prove necessity: Take the functions $f(x)=x^{2}+x, g(x)=x^{2}-x$, neither of which are even functions, but $h(x)=$ $f(x)+g(x)=2 x^{2}$ is an even function.

Therefore, “$f(x) 、 g(x)$ are both even functions” is a sufficient but not necessary condition for “$h(x)=f(x)+g(x)$ is an even function”, the answer is B.