CAT 2017 Slot 1 QA Question & Solution
AlgebraMedium
Question
$f(x) = \frac{5x+2}{3x-5}$ and $g(x) = x^2 - 2x - 1$, then the value of $g(f(f(3)))$ is
Options
2
$\frac{1}{3}$
6
$\frac{2}{3}$
Solution
$f(3) = \frac{15 + 2}{9 - 5} = \frac{17}{4}$
$f(f(3)) = \frac{5*17/4 + 2}{3*17/4 - 5} = \frac{93/4}{31/4} = \frac{93}{31} = 3$
$g(f(f(3))) = 3^2 - 3*2 - 1 = 2$