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

Question 33:
$f(x) = \frac{5x+2}{3x-5}$ and $g(x) = x^2 - 2x - 1$, then the value of $g(f(f(3)))$ is

2
$\frac{1}{3}$
6
$\frac{2}{3}$

Option: 1
Explanation:

$f(3) = \frac{15 + 2}{9 - 5} = \frac{17}{4}$
$f(f(3)) = \frac{5×17/4 + 2}{3×17/4 - 5} = \frac{93/4}{31/4} = \frac{93}{31} = 3$
$g(f(f(3))) = 3^2 - 3×2 - 1 = 2$

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CAT 2017 [slot 1] Question with solution 33

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