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Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)

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Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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New post 19 Jan 2015, 05:13
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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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New post 19 Jan 2015, 06:11
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1
Bunuel wrote:
Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)

A. 0
B. 4
C. 6
D. 7
E. 13

Kudos for a correct solution.



2(3x-5) -1 = 3(3x-6) -5
6x-11=9x-18-5
23-11=3x
12 = 3x
x=4

IMO B
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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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New post 19 Jan 2015, 08:30
1
Given f(x) = 3x – 5

2*[f(x)] – 1 = f(3x – 6)

=>2 (3x-5) -1=3(3x-6)-5
=>6x-5=10-1=9x-18-5
=>3x=23-11=12
=>x=4

Answer is B

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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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New post 20 Jan 2015, 02:44
1
Answer = B = 4

f(x) = 3x – 5

2*[f(x)] – 1 = f(3x – 6)

2(3x-5) -1 = 3 (3x-6) - 5

6x - 11 = 9x - 23

x = 4
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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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New post 03 Mar 2015, 07:08
Bunuel wrote:
Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)

A. 0
B. 4
C. 6
D. 7
E. 13

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

We have the function f(x) = 3x – 5, and we want to some sophisticated algebra with it. Let’s look at the two sides of the prompt equation separately. The left side says: 2*[f(x)] – 1 —- this is saying: take f(x), which is equal to its equation, and multiply that by 2 and then subtract 1.
2*[f(x)] – 1 = 2*(3x – 5) – 1 = 6x – 10 – 1 = 6x – 11

The right side says f(3x – 6) — this means, take the algebraic expression (3x – 6) and plug it into the function, as discussed above in the section “How a mathematician things about a function.” This algebraic expression, (3x – 6), must take the place of x on both sides of the function equation.
f(3x – 6)= 3*[3x – 6] – 5 = 9x – 18 – 5 = 9x – 23

Now, set those two equal and solve for x:
9x – 23 = 6x – 11
9x = 6x – 11 + 23
9x = 6x + 12
9x – 6x = 12
3x = 12
x = 4

Answer = B

- See more at: http://magoosh.com/gmat/2012/function-n ... A6v9I.dpuf
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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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New post 12 Apr 2015, 11:07
2(3x-5)-1=3(3x-6)-5
6x-11=9x-23
3x=12
x=4
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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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New post 12 Apr 2015, 20:10
Hi All,

Since this question asks for the value of X that fits a specific set of conditions, and the answer choices are NUMBERS, we can TEST THE ANSWERS. This is essentially a "brute force" solution - we just have to plug in answers until we find the one that fits the given 'restrictions.'

We're told that the f(X) = 3X - 5

We're asked for the value of X that would make 2[f(X)] - 1 = f(3X - 6)

Let's start with Answer A...

IF....
X = 0
f(0) = 0-5 = -5
2[f(0)] - 1 = 2(-5) - 1 = -11
f(-6) = -18 - 5 = -23
-11 is NOT equal to -23 so this is NOT the answer.

Let's try Answer B....

IF....
X = 4
f(4) = 12-5 = 7
2[f(4)] - 1 = 14 - 1 = 13
f(6) = 18 - 5 = 13
13 IS equal to 13, so this MUST be the answer.

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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)  [#permalink]

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Re: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)   [#permalink] 08 Aug 2018, 05:58
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