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# The function f is defined by subtracting 25 from the square of a numbe

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Intern
Joined: 24 Jul 2009
Posts: 29
The function f is defined by subtracting 25 from the square of a numbe  [#permalink]

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16 Aug 2011, 15:36
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Difficulty:

25% (medium)

Question Stats:

79% (02:04) correct 21% (02:20) wrong based on 114 sessions

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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!
Director
Joined: 01 Feb 2011
Posts: 629
Re: The function f is defined by subtracting 25 from the square of a numbe  [#permalink]

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16 Aug 2011, 18:46
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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

Manager
Joined: 18 Mar 2010
Posts: 77
Location: United States
Re: The function f is defined by subtracting 25 from the square of a numbe  [#permalink]

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16 Aug 2011, 19:49
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."
Intern
Joined: 24 Jul 2009
Posts: 29
Re: The function f is defined by subtracting 25 from the square of a numbe  [#permalink]

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16 Aug 2011, 21:18
@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.
Intern
Joined: 24 Jun 2018
Posts: 2
Re: The function f is defined by subtracting 25 from the square of a numbe  [#permalink]

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18 Jun 2019, 12:31
how x= -15 is valid in this question, g, in that case, would not be valid
Re: The function f is defined by subtracting 25 from the square of a numbe   [#permalink] 18 Jun 2019, 12:31
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