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If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the

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zxcvbnmas
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If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the [#permalink] New post   04 Feb 2016, 17:57
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If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the following is a possible value of g(f(x))?


A) -23

B) -17

C) 0

D) 8

E) 20
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A
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chetan2u
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Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the [#permalink] New post   04 Feb 2016, 19:05
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zxcvbnmas wrote:
If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the following is a possible value of g(f(x))?


A) -23

B) -17

C) 0

D) 8

E) 20


Hi,
You have two functions and you are asked to find function of the first function.
So substitute fx for x...
G(x)=2x+3...
F(x)=4x-1...
So g(f(x))=2(4x-1)+3=8x-2+3=8x+1...
If you look at the choices only A is in this format..
8*(-3)+1=-23....
A
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Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the [#permalink] New post   04 Feb 2016, 21:14
Expert Reply
zxcvbnmas wrote:
If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the following is a possible value of g(f(x))?


A) -23

B) -17

C) 0

D) 8

E) 20


f(x)=4x−1 and g(x)=2x+3

g(f(x)) = 2*f(x)+3 = 2*(4x-1)+3 = 8x+1 i.e. a Multiple of 8+1


Checking Options

-23 = 8*(-4)+1 hence CORRECT ANSWER

Answer: option A
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Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the [#permalink] New post   16 Aug 2017, 03:06
GMATinsight 8*-4 will be -32 not -24
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Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the [#permalink] New post   17 Sep 2018, 22:11
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zxcvbnmas wrote:
If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the following is a possible value of g(f(x))?


A) -23

B) -17

C) 0

D) 8

E) 20


g(f(x)) will be the same as g(4x - 1).
So wherever we have x in g(x), we just substitute it with (4x - 1)

g(f(x)) = 2*(4x - 1) + 3 = 8x + 1

A possible value of g(x) is x is an integer is 1 more than a multiple of 8.
-24 is a multiple of 8 and -24 + 1 = -23
No other option is 1 more than a multiple of 8.

Answer (A)

For more on functions, check:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... s-on-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... questions/
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Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the [#permalink] New post   02 Dec 2020, 13:16
zxcvbnmas wrote:
If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the following is a possible value of g(f(x))?


A) -23

B) -17

C) 0

D) 8

E) 20


\(g(f(x)) = g(4x−1) = 2(4x−1) + 3 = 8x + 1\)

So we're looking for a multiple of 8 plus 1. Lets check the options:

\(8(-3) + 1 = -23\)

Answer is A.
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Re: If f(x)=4x1 and g(x)=2x+3 for all integers, which of the [#permalink] New post   30 Aug 2023, 02:52
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Re: If f(x)=4x1 and g(x)=2x+3 for all integers, which of the [#permalink]
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