# CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

###### CAT Questions | Algebra | Functions - Function of a function CAT Questions

The question is about Function of a function. We need to find out the value of function of a function at x = 3. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 10: x is a real number such that f(x) = $$frac{1}{x}\\$ when x > 0 and f$x) = $$frac{1}{x + 1}\\$ otherwise. Also fn$x) = f(fn - 1 (x)). What is f(3) + f2(-3) + f3(3) + f4(-3)?

1. $$frac{-2}{3}\\$ 2. $\frac{14}{3}\\$ 3. 0 4. 3 ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from CAT Algebra - Functions: Substitute x = 3 or x = -3 as appropriate for the function of a function and get the values. f$x) = $$frac{1}{x}\\$ when x > 0; f$x) = $$frac{1}{x + 1}\\$ otherwise f$3) = $$frac{1}{3}\\$ f$-3) = $$frac{-1}{2}\\$ f2$3) = f(f(3) = f($$frac{1}{3}\\$) = 3 f2$-3) = f(f(-3) = f($$frac{-1}{2}\\$) = $\frac{1}{$-1/2 + 1$}$ = 2 f$3) + f2(-3) + f3(3) + f4(-3)
= $$frac{1}{3}\\$ + f$f1(-3)) + f(f2(3)) + f(f3(-3))
= $$frac{1}{3}\\$ + f$$$frac{-1}{2}\\$ + f$3) + f(f(f2(-3)))
= $$frac{1}{3}\\$ + 2 + $\frac{1}{3}\\$ + f$f(2))
= $$frac{8}{3}\\$ + f[$\frac{1}{2}\\$] = $\frac{8}{3}\\$ + 2 = $\frac{14}{3}\\$ The question is "What is f$3) + f2(-3) + f3(3) + f4(-3)?"

##### Hence the answer is " $$frac{14}{3}\\$" Choice B is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Coaching | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Functions Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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