Hi guys,
Need a little help here.
For which of the following functions 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) = (square root of x)
d) f(x) = 2/x
e) f(x) = -3x
Function Question
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Easiest method to solve this is to use the concept of linearity. If f(a + b) = f(a) + f(b), then the function f(x) must be linear. Only option B and E are linear functions. Now check them individually.actofman wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
For option B, f(a) = (a + 1) and f(b) = (b + 1).
So, f(a) + f(b) = (a + b + 2). But f(a + b) = (a + b + 1) ≠f(a) + f(b)
Then option E is our only choice.
The correct answer is E.
Anju Agarwal
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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 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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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