For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers of a & b.
A). f(x) = x squared
B). f(x) = x + 1
C). f(x) = sq root of x
D). f(x) = 2/x
E). f(x) = -3x
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GMATGuruNY
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Let a=2 and b=3.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
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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Another approach is to let a = 1 and b = 1 and plug in the values.For which of the following functions f(a+b) = f(a) + f(b) for all positive numbers a and b?
f(x)= x²
f(x)= x+1
f(x)= √x
f(x)= 2/x
f(x)= -3x
So, the question becomes, "Which of the following functions are such that f(1+1) = f(1) + f(1)?"
In other words, for which function does f(2) = f(1) + f(1)?
A) If f(x)=x², does f(2) = f(1) + f(1)?
Plug in to get: 2² = 1² + 1²? (No, doesn't work)
So, it is not the case that f(2) = f(1) + f(1), when f(x)=x²
B) If f(x)=x+1, does f(2) = f(1) + f(1)?
Plug in to get: 2+1 = 1+1 + 1+1? (No, doesn't work)
So, it is not the case that f(2) = f(1) + f(1)
.
.
.
A, B, C and D do not work.
NOTE: at this point, we can conclude that E MUST be the correct answer. In a test situation, I might save time and not bother checking E.
But, let's check E anyway (for "fun")
E) If f(x)=-3x, does f(2) = f(1) + f(1)?
Plugging in 2 and 1 we get: (-3)(2) = (-3)(1) + (-3)(1)
Yes, it works
The correct answer is E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
