arjunshn wrote:For which of the following function f(a+b)=f(a)+f(b) for all positive numbers a and b?
f(x)=x^2
f(x)=x+1
f(x)=rootx
f(x)=2/x
f(x)=-3x
Plug in a=2 and b=3. Thus, a+b=5. The question becomes:
For which of the following functions does f(5) = f(2) + f(3)?
Look for the answer choice most likely to work:
Answer choice E: f(x) = -3x
f(5) = -3*5 = -15.
f(2) = -3*2 = -6.
f(3) = -3*3 = -9.
-15 = -6 + -9.
Success!
The correct answer is
E.
A quick glance at the other answer choices tells me that they won't work. Anyone not sure about an answer choice should do the math:
Answer choice A: f(x) = x^2
f(5) = 5^2 = 25.
f(2) = 2^2 = 4.
f(3) = 3^2 = 9.
25 = 4+9.
Doesn't work. Eliminate A.
Answer choice B: f(x) = x+1
f(5) = 5+1 = 6.
f(2) = 2+1 = 3.
f(3) = 3+1 = 4.
6 = 3+4.
Doesn't work. Eliminate B.
Answer choice C: f(x) = √x
f(5) = √5
f(2) = √2
f(3) = √3
√5 = √2+√3.
Doesn't work. Eliminate C.
Answer choice D: f(x) = 2/x
f(5) = 2/5.
f(2) = 2/2 = 1.
f(3) = 2/3.
2/5 = 1 + 2/3.
Doesn't work. Eliminate D.
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