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# If f(2x - 1) = 4x² - 4x - 8, then f(5) =

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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
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f(2x-1)= f(5); when x=3

Put x=3 in the equation 4$$x^2$$ -4x - 8. The answer is 16.

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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
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GMATPrepNow wrote:
If f(2x - 1) = 4x² - 4x - 8, then f(5) =

A) 16
B) 18
C) 36
D) 48
E) 72

Another way.. May help in such questions somewhere else..

If you look at the equation, you can easily convert the equation ...
$$f(2x-1)=4x^2-4x-8=4x^2-4x+1-9=(2x-1)^2-9$$
So it can be literally written as $$f(x)=x^2-9$$,
So f (5)=5^2-9=25-9=16
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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
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Equate 2x-1 = 5 you get x=3
Put x=3 36-8-12
16

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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
OA: A

f(2x - 1) = 4x² - 4x - 8, then f(5) = ?

Trying lengthier method as other methods have been already discussed above

Let $$2x-1 =y ; x =\frac{y+1}{2}$$

$$f(y) = 4(\frac{y+1}{2})^2 -4 (\frac{y+1}{2}) -8 =(y+1)^2-2(y+1)-8 =y^2+1+2y-2y-2-8=y^2-9$$

$$f(y)=y^2-9$$

$$f(5) =5^2-9=25-9=16$$
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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
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GMATPrepNow wrote:
If f(2x - 1) = 4x² - 4x - 8, then f(5) =

A) 16
B) 18
C) 36
D) 48
E) 72

to find f(5), never go ahead and put the value as 5 in f(2x-1)

Think how can i get a f(5), when i substitute x = 3

f(5) =36 - 20
= 16

A
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If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
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GMATPrepNow wrote:
If f(2x - 1) = 4x² - 4x - 8, then f(5) =

A) 16
B) 18
C) 36
D) 48
E) 72

Great responses above!! Here's one more approach:

First notice that 4x² - 4x - 8 looks a lot like (2x - 1)²

(2x - 1)² = (2x - 1)(2x - 1) = 4x² - 4x + 1

Now take: f(2x - 1) = 4x² - 4x - 8
Rewrite as: f(2x - 1) = 4x² - 4x + 1 - 9 = (2x - 1)² - 9
In other words, f(something) =something² - 9

In general, we can write f(x) = x² - 9

So f(5) = 5² - 9 = 25 - 9 = 16

Cheers,
Brent
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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
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Re: If f(2x - 1) = 4x² - 4x - 8, then f(5) = [#permalink]
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