Questions about the world of GMAT Math from other sources and general math related questions.
kant.manu
Students
 
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Question on Function - Manhattan GMAT Guide #3

by kant.manu Sat Oct 31, 2009 7:52 pm

I went through Manhattan GMAT Guide #3 Chapter 5 - Function where I found Question #2 in the Problem Set a little confusing. The question says:

If g(x) = 3x+x^(1/2), what is the value of g(d^2 + 6d + 9).

In this case, the solution says:
g(d^2 + 6d + 9) = 3(d^2 + 6d + 9)+ (d^2 + 6d + 9)^1/2
3d^2 +18d+27 + sq.rt [(d+3)^2]

3d^2 +18d+27 + d+3 OR 3d^2 +18d+27 -(d+3)
3d^2 +19d+30 OR 3d^2 +19d+24
(if d+3 >=0) OR (if d+3 <=0) [Didn't understand this part quite well]

Other question is: if we are considering + and - signs while taking roots, why are we not taking them into consideration in Question 4 of the same exercise.

Could anyone please clarify from Manhattan GMAT faculty?
Ben Ku
ManhattanGMAT Staff
 
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Joined: Sat Nov 03, 2007 7:49 pm
 

Re: Question on Function - Manhattan GMAT Guide #3

by Ben Ku Thu Nov 19, 2009 5:00 am

basically your question comes down to simplifying
sqrt((d + 3)^2)

Let's look at a simpler example. If I told you that

sqrt( x^2) = 5

Here, x is either 5 or -5, because when we squared x, we lost the negative sign. So when we simplify sqrt((d + 3)^2), we don't know whether d + 3 was originally positive or negative. So we have to take into account both situations.

In question #4, we don't consider positive and negative solutions because we are told in the beginning that x = 4.

By the way, questions from our Strategy Guide should really be placed in our Strategy Guide folders, and not in the General Math folder.
Ben Ku
Instructor
ManhattanGMAT