rsarashi wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positives numbers a and b?
A) f(x) = x²
B) f(x) = x+1
C) f(x) = under root x
D) f(x) = 2/x
E) f(x) = -3x
OAE[/spoiler]
We need to determine when f(a + b) = f(a) + f(b). We can determine the correct answer choice by substituting numerical values for a and b. We could use any two values for a and b, but for simplicity, let's choose a = 1 and b = 2. The function now looks like this:
f(1 + 2) = f(1) + f(2)
f(3) = f(1) + f(2)
So, we must determine which answer choice(s) has f(3) equal to the sum of f(1) and f(2).
Let's evaluate each answer choice.
A) f(x) = x^2
f(3) = 3^2 = 9
f(1) = 1^2 = 1
f(2) = 2^2 = 4
Since 9 does not equal 1 + 4, choice A is not correct.
B) f(x) = x + 1
f(3) = 3 + 1 = 4
f(1) = 1 + 1 = 2
f(2) = 2 + 1 = 3
Since 4 does not equal 3 + 2, choice B is not correct.
C) f(x) = √x
f(3) = √3
f(1) = √1 = 1
f(2) = √2
Since √3 does not equal 1 + √2, choice C is not correct.
D) f(x) = 2/x
f(3) = 2/3
f(1) = 2/1 = 2
f(2) = 2/2 = 1
Since 3/2 does not equal 1 + 2, choice D is not correct.
E) f(x) = -3x
f(3) = -3(3) = -9
f(1) = -3(1) = -3
f(2) = -3(2) = -6
Since -9 equals -3 + (-6), choice E is correct.
Answer:
E
