A function f(x) is defined as f(x+y)=f(x)+f(y) for all real value of x and y, and f(1)=5. What is the value of f(3)?

A. 1

B. 5/3

C. 5

D. 10

E. 15

We are only given f(1) = 5. We need to work our way to change the input to x = 3 instead of x = 1. Observe that if we plug in y = x the property becomes f(x + x) = f(x) + f(x), or f(2x) = 2f(x). We can do this again but with y = 2x to get f(x + 2x) = f(x) + f(2x) = f(x) + 2f(x), and we get f(3x) = 3f(x). Now we can plug in x = 1 into this to change the input to 3, f(3*1) = 3*f(1) =3 * 5 = 15.

Ans: E

A. 1

B. 5/3

C. 5

D. 10

E. 15

**Solution:**We are only given f(1) = 5. We need to work our way to change the input to x = 3 instead of x = 1. Observe that if we plug in y = x the property becomes f(x + x) = f(x) + f(x), or f(2x) = 2f(x). We can do this again but with y = 2x to get f(x + 2x) = f(x) + f(2x) = f(x) + 2f(x), and we get f(3x) = 3f(x). Now we can plug in x = 1 into this to change the input to 3, f(3*1) = 3*f(1) =3 * 5 = 15.

Ans: E