in Quantitative Aptitude retagged by
191 views
1 vote
1 vote

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

  1. $2$
  2. $1/3$
  3. $6$
  4. $2/3$
in Quantitative Aptitude retagged by
13.4k points
191 views

1 Answer

1 vote
1 vote
Given that, $f(x) = \frac{5x+2}{3x-5}$

And, $g(x) = x^{2}-2x-1$

Now, $f(3) = \frac{5(3)+2}{3(3)-5} = \frac{17}{4}$

$\Rightarrow  f(f(3)) = f\left(\frac{17}{4}\right)$

$\Rightarrow  f\left(\frac{17}{4}\right) = \frac{5\left(\frac{17}{4}\right)+2}{{3\left(\frac{17}{4}\right)-5}}$

$\Rightarrow  f\left(\frac{17}{4}\right) = \dfrac{\frac{85+8}{4}}{\frac{51-20}{4}}$

$\Rightarrow  f\left(\frac{17}{4}\right) =\frac{93}{31} = 3$

$\Rightarrow  g(f(f(3))) = g\left(f\left(\frac{17}{4}\right)\right) = g(3)$

$\Rightarrow g(3) = 3^{2} – 2(3)-1 = 9-6-1  = 9-7 = 2$   

$\therefore$ The value of $g(f(f(3))) = 2.$

Correct Answer $:\text{A}$
edited by
10.3k points
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true