essential questions

(a)
no, generally f(x+y) not equal to f(x) + f(y)
let f(x)=1
then
f(x+y)=1
f(x) + f(y) =1+1=2
f(x+y) not equal to f(x) + f(y)
The other example is f(x)=sinx
(b)
f(x) = a·bx
f(x+c)
=a·b(x+c)
= f(x) · bc
=a·bx + a·bc
=f(x)+ a·bc
(c)
f(x) = mx+b
f(x+c)
=m(x+c)+b
=mx+mc+b
= f(x)+mc

2007-02-01 16:59:52 補充：
COPY wrongf(x+c)=a·b(x+c) =a·bx + a·bc=f(x)+ a·bc