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Function question

by anthony.j » Sun May 03, 2009 12:46 pm
How would you go about solving this question?

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) = sqrt of x
d - f(x) = 2/x
e - f(x) = -3x

answer is f(x) = -3x

Thanks!
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by artistocrat » Sun May 03, 2009 1:38 pm
f(a+b)=f(a)+f(b)

f(x)=-3x

lets use, a=2 & b=3:

then f(a)=-3(2)=-6
and f(b)=-3(3)=-9

and f(a+b)=f(5)=-15

so definitely f(a+b)=f(a)+f(b)

I hope it helps
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by lilu » Sun May 03, 2009 4:41 pm
https://www.beatthegmat.com/f-a-b-f-a-f-b-t35045.html

DanaJ gives an excellent explanation to this problem in the link attached
The more you look, the more you see.
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Junior | Next Rank: 30 Posts
Posts: 26
Joined: Mon Apr 27, 2009 6:37 am
Location: South NJ, right outside of Philly
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by anthony.j » Sun May 03, 2009 5:12 pm
Awesome! Thank you for the link.

Next time I will try typing the problem in as my search term. Never thought of that. Double thanks!
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