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

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Bunuel
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If f(x) is a linear function, what is the value of f(2)? [#permalink] New post   10 Jul 2017, 04:30
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If f(x) is a linear function, what is the value of f(2)?


(1) \(f(f(x)) = 9x + 8\)

(2) \(f(f(2)) = 26\)
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E
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elainetianfong
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Re: If f(x) is a linear function, what is the value of f(2)? [#permalink] New post   17 Oct 2017, 20:53
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Bunuel wrote:
If f(x) is a linear function, what is the value of f(2)?

(1) f(f(x)) = 9x + 8
(2) f(f(2)) = 26


(1). Let's f(x)= ax +b

=> f(f(x)) = a(ax+b)+b= 9x+8
=> a^2*x + ab +b = 9x+8
=> a^2 = 9 AND ab + b= 8
=> a = 3, b = 2 OR a = -3, b = -4
Insufficient.


(2). f(2) = 2a + b
=> f(f(2)) = a(2a+b) + b = 26
=> 2a^2 + ab + b = 26
Insufficient.

(1) + (2) => With each (a,b) we found in (1), we substituted into (2) and received the same result.
So E is the final answer.
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Re: If f(x) is a linear function, what is the value of f(2)? [#permalink] New post   10 Jul 2017, 05:37
Bunuel wrote:
If f(x) is a linear function, what is the value of f(2)?

(1) f(f(x)) = 9x + 8
(2) f(f(2)) = 26


stat 1: not suff..its a function withing a function and without knowing f(x) it not possible to get the relation

stat2: clearly not suff..

both statements are same,,hence not suff..
ans E
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Re: If f(x) is a linear function, what is the value of f(2)? [#permalink] New post   26 Mar 2020, 05:15
f(f(x)) = 9x+8

lets consider f(x) as 3x+2
then f(f(x)) = 3(3x+2)+2 = 9x+8

then f(2) can be = 3*2+2 = 8.

1st stmt can be sufficient.
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Re: If f(x) is a linear function, what is the value of f(2)? [#permalink]
26 Mar 2020, 05:15
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Bunuel
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