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If g(x) = 3x + sqrt x

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If g(x) = 3x + sqrt x [#permalink]

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If \(g(x) = 3x + \sqrt {x}\), what is the value of \(g(d^2 +6d+9)\)?



(Chapter 5, Page 79 - In Action problem #2)

SEO was poor for this question. Also, this is more open ended practice so it's less GMAT like.

Originally posted by jwam2 on 25 Feb 2016, 15:31.
Last edited by ENGRTOMBA2018 on 25 Feb 2016, 17:08, edited 1 time in total.
Reformatted the question
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Re: If g(x) = 3x + sqrt x [#permalink]

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New post 25 Feb 2016, 19:23
jwamala wrote:
If \(g(x) = 3x + \sqrt {x}\), what is the value of \(g(d^2 +6d+9)\)?



(Chapter 5, Page 79 - In Action problem #2)

SEO was poor for this question. Also, this is more open ended practice so it's less GMAT like.


Hi,
1)\(g(x) = 3x + \sqrt {x}\)..
and \(g(d^2 +6d+9)\)..
so substitute x as d^2 +6d+9..
\(g(d^2 +6d+9) = 3(d^2 +6d+9) + \sqrt {d^2 +6d+9}\)..
\(3d^2+18d+27+d+3=3d^2+19d+30\)

or
2)\(3x + \sqrt {x}=\sqrt {x}(3\sqrt {x}+1)\)...
if\(x= d^2 +6d+9\), \(\sqrt{x}\)=\(\sqrt{(d+3)^2}\)..
\(\sqrt {x}(3\sqrt {x}+1)\)=\(\sqrt{(d+3)^2}(3\sqrt{(d+3)^2}+1)\)..
\(\sqrt{(d+3)^2}(3\sqrt{(d+3)^2}+1)\)...
=\((d+3)(3d+9+1)=(d+3)(3d+10)\)
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If g(x) = 3x + sqrt x [#permalink]

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New post 25 Feb 2016, 19:54
The solutions suggest that "3d^2 + 17d + 24" is also an answer. I'm not fully convinced so I've posted it here.

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Re: If g(x) = 3x + sqrt x [#permalink]

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New post 25 Feb 2016, 20:15
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

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Re: If g(x) = 3x + sqrt x [#permalink]

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New post 25 Feb 2016, 20:19
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jwamala wrote:
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

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As per GMAT,
\(\sqrt{9}= 3\) and not -3..
only if it is given \(\sqrt{9}= |3|\), you take two values 3 and -3..

there must be some thing else given too to take -ive root as an option..

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If g(x) = 3x + sqrt x [#permalink]

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New post 25 Feb 2016, 20:23
I agree with you; that's why I posted the question.

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Re: If g(x) = 3x + sqrt x [#permalink]

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New post 18 Aug 2017, 04:10
chetan2u wrote:
jwamala wrote:
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

Posted from my mobile device


As per GMAT,
\(\sqrt{9}= 3\) and not -3..
only if it is given \(\sqrt{9}= |3|\), you take two values 3 and -3..

there must be some thing else given too to take -ive root as an option..



Is this only as per GMAT or mathematics in General? bunuel?
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Re: If g(x) = 3x + sqrt x [#permalink]

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New post 18 Aug 2017, 04:19
GMP12 wrote:
chetan2u wrote:
jwamala wrote:
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

Posted from my mobile device


As per GMAT,
\(\sqrt{9}= 3\) and not -3..
only if it is given \(\sqrt{9}= |3|\), you take two values 3 and -3..

there must be some thing else given too to take -ive root as an option..



Is this only as per GMAT or mathematics in General? bunuel?


When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. Even roots have only a positive value on the GMAT.

In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5.
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Re: If g(x) = 3x + sqrt x   [#permalink] 18 Aug 2017, 04:19
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