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.Com
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) (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)
RELATED QUESTIONS
if f(a+b) = f(a) + f(b) for all real numbers. Show how f(2a) = 2*f(a) and show how f(0)... (answered by HyperBrain,Doni305)
Dear Sir/Madam;
A pleasant day! Please help me with this Math problem about... (answered by richard1234)
Let f be a continuous function such that f(-1) = -1 and f(1) = 1.
Classify each of the... (answered by robertb)
Let f be a continuous function such that f(-1) = -1 and f(1) = 1.
Classify each of the... (answered by richard1234)
If a and h are real numbers, find the following values for the given function.
f(x) = 7... (answered by stanbon)
Suppose that f(x) = ax + b, where a and b are real numbers.
Given that f(f(f(x))) = 8x... (answered by jim_thompson5910)
Hi, I am having problems understanding a problem based on the rule of a function. The... (answered by ikleyn)
A certain function f has the property that f(x + y) = f(x) + f(y) for all values of x... (answered by robertb)
Suppose f is a function such that f(f(x)) = x for all x in the domain of f, and suppose... (answered by CPhill)