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For which of the following functions is f(a+b) =f(a)+f(b)

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For which of the following functions is f(a+b) =f(a)+f(b) [#permalink] New post 23 Feb 2006, 15:18
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A
B
C
D
E

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1. For which of the following functions is f(a+b) =f(a)+f(b) for all positive numbers a&b

a. f(x)=x^2
b. f(x)=x+1
c. f(x)= sq.rt x
d. f(x)=2/x
e.f(x)=-3x

2.For all positive integers m, @m=3m, when m is odd and @m=1/2m when m is even, which of the following is equivalent to @9X@6

a.81
b.54
c.36
d.27
e.18


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 [#permalink] New post 23 Feb 2006, 19:24
Question 1
a. f(a+b) = (a+b)^2 != f(a)+f(b) = a^2 + b^2
b. f(a+b) = a+b+1 != f(a) + f(b) = a+b+2
c. f(a+b) = sqrt(a+b) != f(a) + f(b) = sqrt(a) + sqrt(b)
d. f(a+b) = -3a-3b = f(a) + f(b) = -3a-3b
Ans D
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 [#permalink] New post 23 Feb 2006, 19:25
Question 2
I assume you mean @9 multiplied by @6.

@9 = 3(9) = 27
@6 = 1/2(6) = 1/12

@9*@6 = 27/12 = 9/4
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 [#permalink] New post 23 Feb 2006, 19:27
As I mentioned in another thread of yours, you might consider posting each question as a different thread in future. It will facilitate discussion tremendously. I hope you have a fantastic learning experience here. =) :wink:
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 [#permalink] New post 24 Feb 2006, 20:57
1. E
2. A

1) f(x) = -3x & f(y) = -3y

f(x+y) = -3(x+y)
= -3x-3y
= -3x + (-3y)
= f(x) + f(y)


2) @9X@6
= 3*9*6*(1/2)
= 81
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 [#permalink] New post 25 Feb 2006, 07:29
Hi

The OA to Q1 is E

For Q2 OA is D i.e 27, i have been banging my head against this problem but cant figure out how it can be 27
  [#permalink] 25 Feb 2006, 07:29
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For which of the following functions is f(a+b) =f(a)+f(b)

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