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A function f has the property that f(3x-1)=x^2+x+1 for all real number

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Bunuel
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A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink] New post   26 Mar 2019, 23:14
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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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itsanujsingh
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink] New post   26 Mar 2019, 23:40
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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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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink] New post   27 Mar 2019, 01:24
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
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink] New post   27 Mar 2019, 03:45
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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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink] New post   28 Mar 2019, 19:07
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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Archit3110
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink] New post   29 Mar 2019, 01:17
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] New post   29 Mar 2019, 08:37
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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

Answer: A
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink] New post   08 Dec 2020, 23:24
Given: A function f has the property that \(f(3x-1)=x^2+x+1\) for all real numbers x.
Asked: What is f(5)?

3x-1 = 5
x = 2

f(5) = 2ˆ2 + 2 + 1 = 7

IMO A
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Re: A function f has the property that f(3x-1)=x^2+x+1 for all real number [#permalink]
08 Dec 2020, 23:24
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