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) = square root of x
F(x) = 2/x
F(x) = -3x
Let a=2 and b=3.
Then f(a+b) = f(2+3) = f(5).
Question stem rephrased:
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.
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.
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