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Function

by cartera » Sat Jan 17, 2009 11:50 pm
What of the following is equivalent to: f(ab)=f(a)f(b)?

A. f(x)=x+1
B.f(x)=1/x
C. f(x)=sqrtx
D. f(x)=3x
E…….


OA B
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by DanaJ » Sat Jan 17, 2009 11:58 pm
I would eliminate A from the start because you have an addition in there, but you're looking for a multiplication.
Now I would just try with B: f(ab) = 1/ab = 1/a *1/b = f(a)*f(b). Since we have a match, I would stop here and make a safe guess...
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by awilhelm » Sun Jan 18, 2009 11:55 am
But sqrt(ab) = sqrt(a) * sqrt(b), no?

Why doesn't option C work?
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by DanaJ » Sun Jan 18, 2009 12:00 pm
Sqrt is a bit of a troublemaker... Since you cannot have a negative number under the sqrt, this could cause some issues. For instance, sqrt[(-5)*(-5)] does not equal sqrt(-5)*sqrt(-5), since sqrt of -5 does not exist.
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by awilhelm » Sun Jan 18, 2009 12:33 pm
Right, thanks.
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