SOLUTION: If f is a function such that f(a+b) = f(a) + f(b), for all real numbers a and b, then show that the following statements are true. a. f(2a) = 2f(a) b.f(-a) = - f(a)

Algebra ->  Rational-functions -> SOLUTION: If f is a function such that f(a+b) = f(a) + f(b), for all real numbers a and b, then show that the following statements are true. a. f(2a) = 2f(a) b.f(-a) = - f(a)       Log On


   

Question 909318: If f is a function such that f(a+b) = f(a) + f(b), for all real numbers a and b, then show that the following statements are true.
a. f(2a) = 2f(a)
b.f(-a) = - f(a)
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
a) f(2a) = f(a+a) = f(a) + f(a) = 2f(a)
b) f(-a) = -f(a) implies that
f(-a) + f(a) = 0
-f(a) + f(a) = 0
so f(-a) = -f(a)