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Master | Next Rank: 500 Posts
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by pkw209 » Thu Dec 10, 2009 5:44 pm
Hi all-

Couldn't figure out this one. Would appreciate a brief explanation. What's the rule for function questions? I know they're pretty simple. thanks!

For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?

1) f(x)=x^2

2) f(x)=x+1

3) f(x) = SQRT(x)

4) f(x)=2 / x

5) f(x)=-3x
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by okigbo » Thu Dec 10, 2009 7:06 pm
I find picking numbers the best approach to these. I'm gonna pick a=3 and b=2

f(a+b) f(a)+f(b)

1) f(x)=x^2 f(5)=x^2=25 f(2)+f(3)=2^2+3^2=4+9=13

2) f(x)=x+1 f(5)=x+1=6 f(2)+f(3)=(2+1)+(3+1)=7

3) f(x) = SQRT(x) f(5)=sq. rt(x)=sq. rt(5) f(2)+f(3)=sq. rt(2)+sq. rt(3)

4) f(x)=2 / x f(5)=2/x=2/5 f(2)+f(3)=2/2 + 2/3

5) f(x)=-3x f(5)=-3(5)=-15 f(2)+f(3)=-3(2)+-3(3)=-6+-9=-15

E is the winner...
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