3. (f + g,h) =["(f(x)+ g(x)h(x) dx= J' f(x)h(x) dx+ f' g(x)h(x) dx=(f,h)+(g,h)4°. (f,J)= J' f(x)dx: (f,f)≥0.: f(x)≥0,且若 f(x)±0，则 f2(x)>0,从而(f,f)>0.故(f,J)=0αf(x)=0.因此，（f,g)为内积，C(a,b)为欧氏空间89.1定义与基本性质§9.1 定义与基本性质 3 . ( , ) ( ) ( ) ( ) ( ) b a f g h f x g x h x dx + = +  ( ) ( ) ( ) ( ) b b a a = + f x h x dx g x h x dx   = + ( , ) ( , ) f h g h 2 4 . ( , ) ( ) b a f f f x dx =  2 f x( ) 0,    ( , ) 0. f f 且若 f x( ) 0,  则 2 f x( ) 0,  从而 ( , ) 0. f f  故 ( , ) 0 ( ) 0. f f f x =  = 因此， ( , ) f g 为内积， C a b ( , ) 为欧氏空间