求助: Prep-Ps-63

sj33333

63.    For which of the following functions is f(a + b) = f(a) + f(b) for all positive numbers a and b ?
(A) f(x) = x 2
(B) f(x) = x + 1
(C) f(x) = √x
(D) f(x) = 2/x
(E) f(x) = -3x
答案为E,但我还是没有想明白为啥?

sj33333

(A) : f(a)=a^2 , f(b)=b^2
f(a+b)=(a+b)^2which is not equal to (a^2) + (b^2) [ f(a) + f(b) ]

(B): f(a)=a+1 , f(b)=b+1 , f(a+b)=a+b+1 which is not equal to (a+1)+(b+1) = a+b+2 [ f(a) + f(b) ]

(C): f(a)= √a , f(b)= √b , f(a+b) = √((a+b) which is not equal to √a+√a [ f(a) + f(b) ]

(D) : f(a)=2/3 , f(b) = 2/3 , f(a+b)=2/3 which is not equal to 2/3 + 2/3 [ f(a) + f(b) ]

(E): f(a)= -3a , f(b)= -3b , f(a+b)= -3(a+b)=(-3a) + (-3b)=f(a) + f(b)