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# If f(x) is a function, what is the value of f(2)?

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Math Expert
Joined: 02 Sep 2009
Posts: 51121
If f(x) is a function, what is the value of f(2)?  [#permalink]

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10 Jul 2017, 03:35
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Difficulty:

65% (hard)

Question Stats:

48% (01:35) correct 52% (02:01) wrong based on 154 sessions

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If f(x) is a function, what is the value of f(2)?

(1) $$(f(x))^2 = 2f(x) − 1$$

(2) $$f(4x) = 8x^2 − 1$$

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Re: If f(x) is a function, what is the value of f(2)?  [#permalink]

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10 Jul 2017, 04:31
stat1: get all the terms on LHS,,,,it will of the form (a-b)^2
implies (f(x) -1)^2 = 0
f(x) = 1,,suff

stat2: suff...
ans D
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Joined: 11 Sep 2015
Posts: 3235
Re: If f(x) is a function, what is the value of f(2)?  [#permalink]

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10 Jul 2017, 05:50
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Bunuel wrote:
If f(x) is a function, what is the value of f(2)?

(1) (f(x))² = 2f(x) − 1

(2) f(4x) = 8x² − 1

Great question, Bunuel!!

Target question: What is the value of f(2)?

NOTE: when I scan the two statements, I see that statement 2 is MUCH easier to deal with. So, let's deal with that first...

Statement 2: f(4x) = 8x² − 1
We want to find the value of f(2)
If we plug in x = 1/2, then 4x = (4)(1/2) = 2
So, we replace x with 1/2 to get: f[(4)(1/2)] = 8(1/2)² − 1
Simplify both sides to get: f(2) = 1.
DONE!!
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Statement 1: (f(x))² = 2f(x) − 1
This LOOKS like it might have the features of a quadratic equation.
To get a better feel, let's let u = f(x)
So, when we take (f(x))² = 2f(x) − 1 and replace f(x) with u we get: u² = 2u - 1
Rearrange to get: u² - 2u + 1 = 0
Factor to get: (u - 1)(u - 1) = 0
Solve to get: u = 1
Now replace u with f(x) to get: f(x) = 1
This tells us that, for ANY value of x, f(x) = 1
So, we can be certain that f(2) = 1.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

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Re: If f(x) is a function, what is the value of f(2)?  [#permalink]

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14 Aug 2018, 12:13
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Re: If f(x) is a function, what is the value of f(2)? &nbs [#permalink] 14 Aug 2018, 12:13
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