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# If f(x) = (5x+2)/(3x−5) and g(x) = x^2 – 2x – 1, then the value of g(f

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Joined: 02 Sep 2009
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If f(x) = (5x+2)/(3x−5) and g(x) = x^2 – 2x – 1, then the value of g(f  [#permalink]

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02 Apr 2020, 10:02
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25% (medium)

Question Stats:

90% (02:05) correct 10% (03:32) wrong based on 20 sessions

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If $$f(x) = \frac{5x+2}{3x−5}$$ and $$g(x) = x^2 – 2x – 1$$, then the value of $$g(f(f(3)))$$ is:

A. 1/3
B. 2/3
C. 1
D. 2
E. 6

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Joined: 12 Dec 2015
Posts: 495
Re: If f(x) = (5x+2)/(3x−5) and g(x) = x^2 – 2x – 1, then the value of g(f  [#permalink]

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02 Apr 2020, 10:18
If $$f(x) = \frac{5x+2}{3x−5}$$ and $$g(x) = x^2 – 2x – 1$$, then the value of $$g(f(f(3)))$$ is:

A. 1/3
B. 2/3
C. 1
D. 2 --> correct: f(3)=$$\frac{5*3+2}{3*3−5}$$ = $$\frac{17}{4}$$, f(f(3))=f(17/4)=$$(5*(17/4)+2)/(3*(17/4)−5)$$ =$$\frac{85+8}{51−20}$$ =$$\frac{93}{31}$$ = 3, so g(f(f(3))) = g(f(17/4)) = g(3) = 3^2-2*3-1=9-6-1=2
E. 6
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Joined: 14 Oct 2019
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Re: If f(x) = (5x+2)/(3x−5) and g(x) = x^2 – 2x – 1, then the value of g(f  [#permalink]

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02 Apr 2020, 10:22
f(x)=5x+2/3x−5 and g(x)=x2–2x–1
f(3)=(5*3+2)/(3*3−5) = 17/4
now, f(17/4) =(5*17/4+2)/(3*17/4−5) = 73/31 = 3
therefore, g(f(f(3))) = g(3) =3^2–2*3–1 = 2

Re: If f(x) = (5x+2)/(3x−5) and g(x) = x^2 – 2x – 1, then the value of g(f   [#permalink] 02 Apr 2020, 10:22