# CAT 2017 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Functions Questions | Question 33

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Question 33 : If f(x) = $$frac{5x + 2}{3x - 5}$ and g$x) = x2 – 2x – 1, then the value of g(f(f(3))) is :

1. 2
2. $$frac{1}{3}$ 3. 6 4. $\frac{2}{3}$ ## 2IIM : Best Online CAT Coaching #### Signup and sample 9 full classes for free The Best Online CAT Coaching Courses ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sun, Feb 23rd, 2020 ### Explanatory Answer ##### Method of solving this CAT Question from Functions Firstly, f$3) = $$frac{5$3$ + 2}{3(3) - 5}) = $$frac{15 + 2}{9 - 5}$ ⟹ f$3) = $$frac{17}{4}$ Now, let us find f$f(3))
f(f(3)) = $$frac{5$$frac{17}{4}$) + 2}{3$$frac{17}{4})) - 5}) = $\frac{\frac{85 + 8}{4}}{\frac{51 - 20}{4}}$ = $\frac{93}{31}$ = 3. Next, we can find g$f(f(3))).
g(f(f(3))) = x2 - 2x - 1
g(f(f(3))) = (x - 1)2 - 2
g(f(f(3))) = (3 - 1)2 - 2 = 4 - 2 = 2

The question is "If f(x) = $$frac{5x + 2}{3x - 5}$ and g$x) = x2 – 2x – 1, then the value of g(f(f(3))) is :"

##### Hence, the answer is 2

Choice A is the correct answer

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