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Function Test OG

by isisalaska » Sun Jan 07, 2007 4:41 pm
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b

f(x)=x^2
f(x)=x+1
f(x)=Sq.root x
f9x)=2/x
f9x)=-3x

Why is -3x?

thanks!
Isis Alaska
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by thankont » Mon Jan 08, 2007 12:10 am
f(a)=-3a, f(b) = -3b, f(a+b) = -3(a+b) = (-3a)+(-3b) = f(a)+f(b)
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by Chrystelle » Fri Jan 12, 2007 5:02 am
Hi guys

I am confused here

f(a)+f(b) = sqrt(a)+sqrt(b) =sqrt(a+b)=f(a+b)

f(a)+f(b) = -3a-3b =-3(a+b) = f(a+b)

That leaves with 2 answers sqrt(x) and -3x
So, which one do we have to choose?
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by aim-wsc » Fri Jan 12, 2007 6:41 am
Chrystelle wrote:Hi guys

I am confused here

f(a)+f(b) = sqrt(a)+sqrt(b) =sqrt(a+b)=f(a+b)

?

INCORRECT.

sqrt 3 + sqrt 2 IS NOT sqrt 5.

I HOPE YOU GOT MY POINT. :)
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by thankont » Fri Jan 12, 2007 6:44 am
be careful here:
sqrt(4) = 2
sqrt(9) = 3
sqrt(4) + sqrt(9) = 5
but sqrt(4+9) = sqrt(13) <>5
put some values to check
thanx
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by krishnamurthyu » Sat Aug 18, 2007 7:13 pm
f(a) + f(b) f(a+b)
f(x)=x^2 ==> a^2 + b^2 != (a+b)^2
f(x)=x+1 ==> a+1 + b+1 != (a+b)+1
f(x)=Sq.root x ==> Rt(a) + Rt (b) != Rt(a+b)
f(x)=2/x ==> 2/a + 2/b != 2/(a+b)
f(x)=-3x ==> -3a + (-3b) = -3(a+b)
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