Plug in a=2, b=3.For which of the following function is f(a+b)=f(a)+f(b) for all positive numbers a and b?
(A) f(x)=x^2
(B) f(x)=x+1
(C) f(x)=√x
(D) f(x)=2/x
(E) f(x)=-3x
f(a+b) = f(2+3) = f(5)
Then the question becomes:
For which of the following functions does f(5) = f(2) + f(3)?
Answer choice A:
f(5) = 5² = 25
f(2) = 2² = 4
f(3) = 3² = 9
25 = 4+9 Doesn't work.
Answer choice B:
f(5) = 5+1 = 6
f(2) = 2+1 = 3
f(3) = 3+1 = 4
6 = 3+4 = 7 Doesn't work.
Answer choice C:
f(5) = √5
f(2) = √2
f(3) = √3
√5 = √2 + √3 Doesn't work.
Answer choice D:
f(5) = 2/5
f(2) = 2/2 = 1
f(3) = 2/3
2/5 = 1 + 2/3 Doesn't work.
The correct answer is E.
Answer choice E:
f(5) = -3*5 = -15
f(2) = -3*2 = -6
f(3) = -3*3 = -9
-15 = -6 + -9
Success!
