Problem Solving

For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b??

f(x)=x^2

f(x)=x+1

f(x)=sqrt(x)

f(x)=2/x

f(x)=-3x

you have to do the calculations and then you will see that E satisfy the condition

moneyman wrote:For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b??

f(x)=x^2

f(x)=x+1

f(x)=sqrt(x)

f(x)=2/x

f(x)=-3x

To start choose two numbers for a and b and plug it into the given function to see what it really means. I like to use 1 and 2 because that keeps the math simple. So f(1+2)=f(1)+f(2), so f(3) must equal the sum of f(1) and f(2). Now that we know what to look for start plugging 1,2, and 3 into the given answers. So going to the last, f(x)=-3x we plug in 1 so f(1)=-3*1=-3, f(2)=-3*2=-6 and f(3)=-3*3=-9. Now that we have our values we can compare them with the statement. f(3)=f(1)+f(2), so -9 = -3+-6. So that works.

Answer is E.