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

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Math Expert
Joined: 02 Sep 2009
Posts: 42571

Kudos [?]: 135392 [0], given: 12691

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

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10 Jul 2017, 03:30
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:20) correct 52% (01:27) wrong based on 50 sessions

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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) $$f(f(2)) = 26$$
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135392 [0], given: 12691

Director
Joined: 21 Mar 2016
Posts: 542

Kudos [?]: 7 [0], given: 98

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

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10 Jul 2017, 04:37
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

Kudos [?]: 7 [0], given: 98

Intern
Joined: 14 Nov 2012
Posts: 19

Kudos [?]: 4 [1], given: 223

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

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17 Oct 2017, 19:53
1
KUDOS
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.

Kudos [?]: 4 [1], given: 223

Re: If f(x) is a linear function, what is the value of f(2)?   [#permalink] 17 Oct 2017, 19:53
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