SOLUTION: Dear Sir/Madam; A pleasant day! Please help me with this Math problem about Operations on Functions. Here is the problem: If a function f(a+b)= f(a) + f(b)for real nu

Algebra ->  Rational-functions -> SOLUTION: Dear Sir/Madam; A pleasant day! Please help me with this Math problem about Operations on Functions. Here is the problem: If a function f(a+b)= f(a) + f(b)for real nu      Log On


   

Question 837744: Dear Sir/Madam;
A pleasant day! Please help me with this Math problem about Operations on Functions. Here is the problem:
If a function f(a+b)= f(a) + f(b)for real numbers a and b. Show that each statement is true
a) f(0)=0
b) f(2a)=2f(a)
c) f(-a)= -f(a)
Thank you very much for your help!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
a) Let a = b = 0.
f(0) = f(0) + f(0) --> f(0) = 0

b) Substitute b = a

c) Substitute b = -2a
f(-a) = f(a) + f(-2a)
f(-a) = f(a) + 2f(-a)
Subtract f(-a) from both sides
0 = f(a) + f(-a)
f(-a) = -f(a)