f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?

Question

f(2x-1) = \frac{( x + 2 )}{( x – 2 )} . What is  f(x) ? 
 
 A. f(x) = \frac{( x + 5 )}{( x – 3 )} 
 B. f(x) = \frac{( x - 5 )}{( x + 3 )} 
 C. f(x) = \frac{( x + 5 )}{( x + 3 )} 
 D. f(x) = \frac{( x – 5 )}{( x – 3 )} 
 E. f(x) = \frac{( x + 3 )}{( x – 3 )}

Chethan92 · Answer

f(2x-1) = f(x)
Now we have to replace 2x-1 by x, i.e, 2x-1 = x
then x = 1
f(2x-1) = -3

Now put x = 1 in all the options, Only Option A yields -3.

A is the answer.

Archit3110 · Answer

from given answer options
do plugin of f(x) as f(2x-1)
in option A
we get 
 f(2x-1) = \frac{( x + 2 )}{( x – 2 )}

IMO A

GMATGuruNY · Answer

Let x=1.
Plugging x=1 into  f(2x-1) = \frac{x + 2}{x – 2} , we get:
  f(2*1-1) = \frac{1 + 2}{1 – 2} 
 f(1) = -3

When x=1, the question stem becomes:
What is  f(1) ?
Since f(1) = -3, the correct answer must yield -3 when x=1.
Only A works:
 f(1) = \frac{1 + 5}{1-3}  = -3

A

fskilnik · Answer

? = f\left( x \right)

f\left( {2x - 1} \right) = {{x + 2} \over {x - 2}}\,\,\,\,\,\left( * \right)

2x - 1 = y\,\,\,\,\, \Rightarrow \,\,\,\,x = {{y + 1} \over 2}

\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,f\left( y \right)\,\, = \,\,{{{{y + 1} \over 2} + 2} \over {{{y + 1} \over 2} - 2}}\,\, = \,\,{{y + 1 + 4} \over {y + 1 - 4}} = {{y + 5} \over {y - 3}}

?\,\,\,:\,\,\,f\left( y \right) = {{y + 5} \over {y - 3}}\,\,\,\,\,\,\,\left

The correct answer is therefore (A).

We follow the notations and rationale taught in the  GMATH  method.

Regards, 
Fabio.

MathRevolution · Answer

=>

We solve this problem using a change of variable. Let  t = 2x -1. 
Then  2x = t + 1  or  x = \frac{( t + 1 )}{2.} 
 f(2x-1) = f(t) = ( (t+1)/2 + 2 ) / ( (t+1)/2 – 2 ) = ( t + 1 + 4 ) / ( t + 1 – 4 ) (after multiplying both top and bottom by 2) 
 = \frac{( t + 5 )}{( t – 3 ).} 
Making the substitution  t = x  gives 
 f(x) = \frac{( x + 5 )}{( x – 3 )}.

Therefore, the answer is A.
Answer: A

ScottTargetTestPrep · Answer

Let y = 2x - 1, so x = (y + 1)/2. In other words,

f(y) =   /

f(y) = (y + 1 + 4) / (y + 1 - 4)

f(y) = (y + 5) / (y - 3)

Now we can replace y with x and obtain:

f(x) = (x + 5) / (x - 3)

Alternate Solution:

First, let’s take x = -2 in f(2x - 1) = (x + 2) / (x - 2):

f( 2(-2) - 1) = (-2 + 2) / (-2 - 2)

f( -5) = 0

Looking at the answer choices, we observe that only A and C equal zero when x = -5; therefore we eliminate B, D and E.

Next, let’s take x = 3 in f(2x - 1) = (x + 2) / (x - 2):

f( 2(3) - 1) = (3 + 2) / (3 - 2)

f(5) = 5

In answer choice C, when we take x = 5, we obtain f(5) = 10/8, which is not equal to 5. Therefore, we eliminate C as well. The only remaining answer choice is A. Indeed, for the function in A, if we take x = 5, we obtain f(5) = (5 + 5) / (5 - 3) = 10/2 = 5.

Answer: A

BrushMyQuant · Answer

Given that  f(2x-1) = \frac{( x + 2 )}{( x – 2 )}  and we need to find the value of  f(x)

To find the value of f(x) we need to compare what is inside the bracket in f(x) and f(2x-1)
=> to find f(x) we need to replace 2x-1 with x in f(2x-1)
=> 2x - 1 to be replaced with X
=> 2x-1 = X
=> x =  \frac{X + 1}{2}

=> f(X) = (  \frac{X+1}{2} + 2  ) / (  \frac{X+1}{2} – 2  )
=> f(X) =  \frac{X+1+2*2}{2}  /  \frac{X+1-2*2}{2}  
=> f(X) =  \frac{X+5}{2}  /  \frac{X-3}{2} 
=> f(X) =  \frac{X+5}{X-3}

So,  Answer will be A 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards