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Root rule question

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Intern
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Joined: 24 Jul 2009
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Root rule question [#permalink] New post 16 Aug 2011, 14:36
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

57% (02:32) correct 43% (01:21) wrong based on 7 sessions
So here is the question:

The function f is defined by subtracting 25 from the square of a number and the function g is defined as the square root of one-half of a number. If g(f(x))=10, then which of the following is a possible value of x?


a) -15
b)-5
c) 0
d) 5
e) 25

My question is when setting up part of the equation, should I take [/square_root](x/2) or the [/square_root]of x and then divide two...does the root encompass both the numerator and denominator. In my mind, it encompasses both and when I take root two to the other side, I don't get the official answer. What am I not understanding correctly? I'm just brushing up on math rules and would appreciate any help!
[Reveal] Spoiler: OA
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Director
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Re: Root rule question [#permalink] New post 16 Aug 2011, 17:46
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f(x) = x^2-25
g(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).

g(f(x)) = 10

g(x^2-25) =10

sqrt((x^2-25)/2) = 10

=> (x^2-25)/2 = 100
=>x^2 = 225

=> x = 15 or -15

Answer is A.
Manager
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Re: Root rule question [#permalink] New post 16 Aug 2011, 18:49
leadout1 wrote:
the square root of one-half of a number.


Agree with Spidy. Would have been the other way if it had read "one half the square root of a number."
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Re: Root rule question [#permalink] New post 16 Aug 2011, 20:18
@mmphf and @spidy001 thanks guys! Yeah, after I went through it one more time I got the right answer...a simple mistake carrying out the equation cost me the answer the first time around.
Re: Root rule question   [#permalink] 16 Aug 2011, 20:18
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