dzelkas wrote:can someone help me explain how to solve this problem?
For which of the following functions is f(a+b)=f(a)+f(b) for al positive numbers a and b?
a) f(x)=x^2
b) f(x)=x+1
c) f(x)= sq root of x
d) f(x)=2/3
e) f(x)=-3x
I will go by each option:
from (A) : f(a)=a^2 , f(b)=b^2 f(a+b)=(a+b)^2 which is not equal to (a^2) + (b^2) [ f(a) + f(b) ]
from (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) ]
from (C): f(a)= sqrt(a) , f(b)=sqrt(b) , f(a+b) = sqrt(a+b ) which is not equal to sqrt(a)+sqrt(b) [ f(a) + f(b) ]
from (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) ]
from (E): f(a)= -3a , f(b)= -3b , f(a+b)= -3(a+b)=(-3a) + (-3b)=f(a) + f(b)
Hence, (E) will be my answer.
