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anchalagarwal: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sat Jun 30, 2012 8:44 pm

by anchalagarwal » Sat Aug 25, 2012 10:44 am

For which of the following functions is f(a+b)=f(b)+f(a) for all positive numbers a and b?
A. f(x)=x2 B. f(x)=x+1 C. f(x)=âˆšx D. f(x)=2/x E. f(x)=-3x

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Source: Beat The GMAT — Problem Solving | Sat Aug 25, 2012 10:44 am

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Aug 25, 2012 10:57 am

anchalagarwal wrote:For which of the following functions is f(a+b)=f(b)+f(a) for all positive numbers a and b?
A. f(x)=x2 B. f(x)=x+1 C. f(x)=âˆšx D. f(x)=2/x E. f(x)=-3x

substitute a for x in each of the choices.
substitute b for x in each of the choices.
add both variables.

a)is a^2 + b^2 = (a+b)^2 ? ---- no

b) is a+1 + b+1 = (a+b) + 1 ? ---- no

c) is a^1/2 + b^1/2 = (a+b)^1/2 --- no

d) is 2/a + 2/b = 2/(a+b) ----- no

e) is -3a + -3b = -3(a+b) ---- yes

ans = [spoiler]e[/spoiler]

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sat Aug 25, 2012 11:36 am

You can also substitute numbers.

For which of the following functions is f(a+b)=f(b)+f(a) for all positive numbers a and b?
A. f(x)=x2 B. f(x)=x+1 C. f(x)=âˆšx D. f(x)=2/x E. f(x)=-3x
Let a = 1 and b = 2
Now the question can be rephrased to For which of the following functions is f(3) = f(1) + f(2) ?
A. f(x)=x^2; f(3)= 9, f(1)+f(2) = 1+4 = 5. 9 is not equal to 5
B. f(x)=x+1; f(3)= 4, f(1)+f(2) = 2+3 = 5. 4 is not equal to 5
C. f(x)=âˆšx; f(3)= âˆš3, f(1)+f(2) = 1+âˆš2 . âˆš3 is not equal to 1+âˆš2
D. f(x)=2/x; f(3)= 2/3, f(1)+f(2) = 2+1 = 3. 2/3 is not equal to 3
E. f(x)=-3x; f(3)= -9, f(1)+f(2) = -3 - 6 = -9. -9 is equal to -9

Anil Gandham
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