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Math Expert V
Joined: 02 Sep 2009
Posts: 56277
If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (01:51) correct 37% (01:40) wrong based on 180 sessions

### HideShow timer Statistics If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x

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Retired Moderator D
Joined: 25 Feb 2013
Posts: 1197
Location: India
GPA: 3.82
If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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5
3
Bunuel wrote:
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x

Statement 1: $$f(x-1) = 2x+4$$, or
$$f(x-1) = 2(x-1)+6$$
therefore $$f(x) = 2x+6$$. but this equation doe not give any value of $$g(x)$$. hence not sufficient

Statement 2: $$f(g(x)) = 4x$$. this does not give any value of function $$f(x)$$. hence not sufficient

Combining 1 & 2 we get
$$f(x) = 2x+6$$, or $$f(g(x)) = 2g(x) + 6$$
$$2g(x)+6 = 4x$$, or $$g(x) = 2x-3$$
therefore $$g(2) = 2*2-3 = 1$$

Option C
##### General Discussion
Director  S
Joined: 21 Mar 2016
Posts: 518
Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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stat1: clearly not suff,,no link to g(x)

stat2: we cannot deduce g(x) from the equation...not suff

combined is sufficient..
use stat1 to get the value of f(x) and then use stat2 to get the value of g(x)

IMO C
Intern  B
Joined: 23 Feb 2017
Posts: 36
Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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I would go with E

may be I am wrong, but, I don't know the equation for g(x) either from stmt 1 or stmt 2.
Intern  B
Joined: 23 Aug 2015
Posts: 23
Location: India
Concentration: General Management, Human Resources
GMAT 1: 610 Q46 V29 GPA: 3
WE: Consulting (Human Resources)
Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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mohshu wrote:
stat1: clearly not suff,,no link to g(x)

stat2: we cannot deduce g(x) from the equation...not suff

combined is sufficient..
use stat1 to get the value of f(x) and then use stat2 to get the value of g(x)

IMO C

Can you please explain how to get g(x) ?
Intern  B
Joined: 27 Apr 2015
Posts: 40
GMAT 1: 370 Q29 V13 Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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1
1
Bunuel wrote:
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x

Given
=> f(x) & g(x) are 2 function. f(2)= ?

Statement 1 f(x-1)=2x+4
=> put x=x+1
=> f(x+1-1)=2(x+1)+4
=> f(x)=2x+6 -------------(1)
Since there is no relation between f(x) & g(x) we cannot find g(2)
Therefore NOT sufficient

Statement 2 f(g(x))=4x
=> f(g(2))=4*2=8
=> f(g(2))=8 -------------(2)
BUT g(2) cannot be found. Therefore NOT sufficient

BOTH Statement 1 & 2
=> f(x)=2x+6 from (1)
=> substituting x=g(2) we have
=> f(g(2))=2g(2)+6
=> But f(g(2))=8 from (2)
=> 8=2g(2)+6
=> 2=2g(2)
=>g(2)=1
Therefore SUFFICIENT

Hence 'C'

Thanks
Intern  B
Joined: 22 Jul 2015
Posts: 4
Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x

Statement (1) - f(x − 1) = 2x + 4

Does not give us any information of g(x)

Not sufficient.

Negate A and D

Statement (2) f(g(x)) = 4x

Does not give any Information of f(x)

Not sufficient.

Negate B

Both Together

We now have equations through which we can find f(x) and g(x) and solve the equation ahead.

Negate E

Equations are solved by the other members in the post.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7599
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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Bunuel wrote:
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables ($$f(x)$$ and $$g(x)$$) and 0 equations, we should consider both conditions 1) & 2) together first.

$$f(g(2)) = 4 \cdot 2 = 8$$ from the condition 2)
From $$f(x-1) = 2x+4$$, we have $$f(x) = 2(x+1)+4 = 2x + 6$$ and $$f(g(2)) = 2 \cdot g(2) + 6 = 8$$
Thus $$2 \cdot g(2) = 2$$ and $$g(2) = 1$$.

Normally, in problems which require 2 or more additional equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Joined: 07 May 2018
Posts: 68
Re: If f(x) and g(x) are two functions, what is the value of g(2)?  [#permalink]

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niks18 wrote:
Bunuel wrote:
If f(x) and g(x) are two functions, what is the value of g(2)?

(1) f(x − 1) = 2x + 4
(2) f(g(x)) = 4x

Statement 1: $$f(x-1) = 2x+4$$, or
$$f(x-1) = 2(x-1)+6$$
therefore $$f(x) = 2x+6$$. but this equation doe not give any value of $$g(x)$$. hence not sufficient

Statement 2: $$f(g(x)) = 4x$$. this does not give any value of function $$f(x)$$. hence not sufficient

Combining 1 & 2 we get
$$f(x) = 2x+6$$, or $$f(g(x)) = 2g(x) + 6$$
$$2g(x)+6 = 4x$$, or $$g(x) = 2x-3$$
therefore $$g(2) = 2*2-3 = 1$$

Option C

SHouldn't the answer for Statement 1 be f(x) = 2x+2. Could you explain how you got 2x+6. Re: If f(x) and g(x) are two functions, what is the value of g(2)?   [#permalink] 22 Jun 2019, 00:05
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