<p>What is the domain of g(x) = squareroot (x^2 - 9)
A) x > -9
B) x > -3
C) |x| <3
D) |x| >3
E) All real numbers</p>
<p>I obviously chose D but Princeton review insists that the answer is E. The explanation at the back of the book does not help at all. In fact, I'm thinking it's a misprint... Anybody?</p>
<p>Thanks in advanced, <3</p>
<p>Yeah I think the answer’s D. I graphed this equation and ended up with no values of x that were between 3 and -3.</p>
<p>Thank you DMOC, I thought so too! :D</p>
<p>If the absolute value of x is less than 3, then g(x) is imaginary, but that is not ruled out by the question unless it stated somewhere that g(x) had to be real also. So the domain could be all real numbers. (If the question about the domain is extended to the complex plane, then it gets a little tricky.)</p>
<p>Hmmm but would you really chose that for an answer?</p>
<p>This is the PR explanation to choice E:</p>
<p>When dealing with ranges of values in the answer choices, plug in numbers that appear in some, but not all, of the ranges in the answer choices. This allows you to use POE. For example, if x= -5, then g(-5) = sqrt ((-5)^2 - 9) = 4. Since you can plug in -5 into the function w/o any problem, -5 is in the domain of g, so eliminate answers that exclude -5. Eliminate (B) and (C).
Now plug in -10 for x. -10 works, so eliminate (A), which doesn’t include -10.
Plugging in x = 0 also works, which elimates (D), leaving you with (E). Another option is to graph the function on a graphing calculator and look for the values of x that are and are not allowed.</p>
<p>^you;re wrong. You can’t plug in 0 in the squ. rt. of (x^2-9) because it comes out to a negative radical, which is undef. Therefore, ZERO DOES NOT WORK. The PR is stupid and doens’t know anything when it comes to the SAT’s. The answer is indeed D.</p>
<p>He’s not wrong, the PR book is wrong. :)</p>
<p>You’re right you can’t put in 0.</p>
<p>Princeton Review create inaccurate problems? Never.</p>
<p>why? A company with such prominence doesn’t take the time to go over the questions for a second time. They should go over it 5 times with 5 different people… So disappointing.</p>
<p>It’s obviously D. Domains include only real numbers.</p>
<p>It’s a she! Why do people automatically assume I’m a guy :p</p>
<p>But yeah this question is from the 2007 PR book, I was too lazy to buy the newer version. The 2009 Kaplan was too painful to read through (too many typos) But I heard that the PR math questions are actually harder! I kinda doubt that though because I complete every maths section with 7 minutes left and 1 question wrong max… I don’t remember ever doing that on the sat. Or maybe I’ve improved, lol!</p>
<p>Plug in x = 0. You obtain squareroot(-9), which is 3i.
If the question does not state that g(x) must be real, there is nothing wrong with 3i as a possibility.
You must have covered complex numbers?</p>
<p>In the context of the regular SAT, no knowledge of complex numbers is assumed or tested, so the answer in an SAT prep book should be D (and I think PR has a typo).</p>
<p>QM in principle is right, and the question should properly say that g(x) is a real-valued function, but again, this is the regular SAT. See page 256 of the Blue Book (middle of page) for a similar example from the test makers.</p>
<p>Interesting, fignewton–and sort of wild that they don’t cover complex numbers now, since they have extended the math range to 2 years of algebra + 1 of geometry. We gave away our blue book after QMP finished testing, so can’t look up the analogous example.</p>
<p>Sideline question: Is the “>” actually “> or equal to”? x = 3 does work, even in the reals only.</p>
<p>Yeah I don’t think the SAT has ever tested anything on imaginary numbers… 
It’s just >, not > and equal to!</p>
<p>A domain can only include real numbers by definition. This remains true even on Math II subject tests when some problems do indeed deal with imaginary numbers.</p>
<p>I’d go with the College Board instructions vis a vis real only vs. complex. Actually, I doubt that this problem would appear on the SAT I or II.</p>
<p>Alright, thank you guys so much! I can always count on college confidential to do the job of a free and smart tutor :p</p>
<p>The SAT (College Board) does not test knowledge regarding domain, range, or imaginary numbers in a formal setting. However, knowledge of the domain or range in a function may help you to solve a problem quicker and/or more effectively.</p>
<p>^I’ve seen SAT problems which ask specifically about the domain and/or range of a function.
I’ll try to find a specific example…</p>