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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the

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Manager  Joined: 06 Jun 2014
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Location: United States
Concentration: Finance, General Management
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If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 74% (01:31) correct 26% (01:49) wrong based on 180 sessions

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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
Math Expert V
Joined: 02 Aug 2009
Posts: 8287
Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the  [#permalink]

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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]

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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

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

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Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the  [#permalink]

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GMATinsight 8*-4 will be -32 not -24
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the  [#permalink]

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1
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.

For more on functions, check:
https://www.veritasprep.com/blog/2015/0 ... s-on-gmat/
https://www.veritasprep.com/blog/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]

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_________________ Re: If f(x)=4x−1 and g(x)=2x+3 for all integers, which of the   [#permalink] 29 Nov 2019, 08:05
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