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Math Expert V
Joined: 02 Sep 2009
Posts: 58454
A function f has the property that f(3x-1)=x^2+x+1 for all real number  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 63% (00:40) correct 38% (01:17) wrong based on 56 sessions

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A function f has the property that $$f(3x-1)=x^2+x+1$$ for all real numbers x. What is f(5)?

(A) 7
(B) 13
(C) 31
(D) 111
(E) 211

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Joined: 27 Sep 2018
Posts: 37
Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number  [#permalink]

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We can write f(5) as f(3*2-1)
Now comparing with f(3x−1)=x^2+x+1
We get x=2
Putting in given equation we have 2^2+2+1=7

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Concentration: Sustainability, Marketing
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number  [#permalink]

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Bunuel wrote:
A function f has the property that $$f(3x-1)=x^2+x+1$$ for all real numbers x. What is f(5)?

(A) 7
(B) 13
(C) 31
(D) 111
(E) 211

f(3x-1)= f(5)
at x= 2
so x^2+x+1 = 7 at x=2
IMOA
Manager  P
Joined: 04 Oct 2018
Posts: 159
Location: Viet Nam
Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number  [#permalink]

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Bunuel wrote:
A function f has the property that $$f(3x-1)=x^2+x+1$$ for all real numbers x. What is f(5)?

(A) 7
(B) 13
(C) 31
(D) 111
(E) 211

f(5) = f(3*2 - 1) = 2^2 + 2 + 1 = 7. Thus A
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Joined: 12 Sep 2017
Posts: 302
Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number  [#permalink]

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Archit3110 wrote:
Bunuel wrote:
A function f has the property that $$f(3x-1)=x^2+x+1$$ for all real numbers x. What is f(5)?

(A) 7
(B) 13
(C) 31
(D) 111
(E) 211

f(3x-1)= f(5)
at x= 2
so x^2+x+1 = 7 at x=2
IMOA

Hello Archit3110!!!

It took me some time to realize that I could equal both functions. ¿In which cases can we do this?

Kind regards!
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Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number  [#permalink]

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jfranciscocuencag wrote:
Archit3110 wrote:
Bunuel wrote:
A function f has the property that $$f(3x-1)=x^2+x+1$$ for all real numbers x. What is f(5)?

(A) 7
(B) 13
(C) 31
(D) 111
(E) 211

f(3x-1)= f(5)
at x= 2
so x^2+x+1 = 7 at x=2
IMOA

Hello Archit3110!!!

It took me some time to realize that I could equal both functions. ¿In which cases can we do this?

Kind regards!

jfranciscocuencag
well the only way to solve this question was to simplify the f(3x-1) ; such that it becomes equal to f(5). so x=2 was substituted
it all depends on the question and the function formula and whats been asked..
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number  [#permalink]

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Bunuel wrote:
A function f has the property that $$f(3x-1)=x^2+x+1$$ for all real numbers x. What is f(5)?

(A) 7
(B) 13
(C) 31
(D) 111
(E) 211

Since we want f(5), we should look for the value of x such that 3x - 1 = 5:

3x - 1 = 5

3x = 6

x = 2, so we have:

f(5) = f(3*2 - 1) = 2^2 + 2 + 1 = 7

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number   [#permalink] 29 Mar 2019, 08:37
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