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function malfunction

by jzw » Sat Mar 03, 2012 12:03 pm
I don't get what I'm not getting. I do understand the concept of functions, they don't "scare me" per se, but I can't understand why the answer choice is D and not A. Meaning, doesn't 1/1/6 become 6? Because you multiply the numerator and denominator by 6/1 in order to get rid of the 1/ ?
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by bajjuri6 » Sat Mar 03, 2012 12:27 pm
I think it may be easier if you tear up the problem into smaller bits. For this particular one, you must find g(2) and g(x) first. g(x) is given.

=> 1/g(x) = (x - 1) / (x^2 + 2)

g(2) = ((2^2) + 2)/(2-1) = 6

=> 1/g(2) = 1/6

So, 1/g(2) * 1/g(x) = (1/6) * (x-1)/(x^2 + 2)

So, the 6 must be in the denominator. Hope this helps.
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by jzw » Sat Mar 03, 2012 12:46 pm
thanks for the response. i realized somewhere between my post and you're response that it was just careless math on my part which contributed to the error. thanks!
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by GMATGuruNY » Sat Mar 03, 2012 12:49 pm
jzw wrote:I don't get what I'm not getting. I do understand the concept of functions, they don't "scare me" per se, but I can't understand why the answer choice is D and not A. Meaning, doesn't 1/1/6 become 6? Because you multiply the numerator and denominator by 6/1 in order to get rid of the 1/ ?
Let x=2.
Then g(x) = g(2) = (2² + 2)/(2-1) = 6.
Thus, 1/(g(2)) * 1/(g(x)) = 1/6 * 1/6 = 1/36. This is our target.

Now we plug x=2 into the answers to see which yields our target of 1/36.
Only answer choice D works:
(x-1) / 6(x²+2) = (2-1) / 6(2²+2) = 1/36.

The correct answer is D.
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by jzw » Sat Mar 03, 2012 5:01 pm
GMATGuruNY wrote:Thus, 1/(g(2))= 1/6
REALLY happy to do plugging in here instead of solving "normally". But how is 1/(g(2)) = 1/6 ?

I get everything else - just this part is messing me up. I would have thought this becomes 12 (6 x 2). What am I missing? Thanks again, in advance.
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by alexander.vien » Mon Jan 21, 2013 5:34 pm
If you think the answer choice is A, then I think the step that you're missing is on the second function, 1/g(x).

When we plug in (x^2+2)/(x-1) into 1/g(x) it's equivalent to division, so we must flip the expression and multiply it by 1 (also known as taking the reciprocal). Thus, we have (x-1)/(x^2+2).

To get 1/g(2) we must simply plug in 2 into the expression and then put a 1 over the result. So,

(2^2 + 2)/(2-1) = 6

So, g(2) = 6

Putting all this information together, 1/6 * (x-1)/(x^2+2) = (x-1)/6(x^2+2)

Answer choice D
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by buzzdeepak » Tue Jan 22, 2013 11:20 am
g(2) = 6 (substituting x = 2 in the given equation)

Therefore, 1/g(2) * 1/g(x) = 1 / 6 * (x-1) / (x^2 + 2) = (x-1) / (6*(x^2 + 2))

Remember that both are reciprocals of the original equation. I think that's the only catch.

(Another method is compute g(2)*g(x) = 6 * given function and take reciprocal.)
Hope this helps...
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