Join WhatsApp Icon CAT WhatsApp Group
Question 155

The set of all positive integers is the union of two disjoint subsets:

{f(1), f(2),.....f(n), ...} and {g(1),g(2).... ,g(n).....}, where f(1) < f(2) <.....< f(n)..., and g(1) < g(2) < ..... < g(n) ...,and

g(n) = f(f(n))+1 for all n >= 1. What is the value of g(1)?

Solution
Share

The union of the two sets is the set of positive integers. Also, given the increasing nature of elements, either f(1) or g(1) must be equal to 1. If g(1) = 1, then f(f(1)) =0 which cannot be under the given conditions.

Hence, f(1) = 1

g(1) = f(f(1))+1 = 2

View More Questions From Functions, Graphs and Statistics

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 38+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Arithmetic QuestionsCAT Simple Interest Compound Interest QuestionsCAT Linear Equations QuestionsCAT Time And Work QuestionsCAT Logarithms, Surds and Indices Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Coins and Weights QuestionsCAT Selection With Condition QuestionsCAT DI with connected data sets QuestionsCAT Truth Lie Concept QuestionsCAT Table based DI Sets Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Verbal Ability QuestionsCAT Grammar and Sentence Correction QuestionsCAT Critical Reasoning QuestionsCAT Para Jumbles QuestionsCAT Para Summary Questions

Free CAT Quant Questions

CAT Quadratic Equations

CAT Logarithms

CAT Inequalities

CAT Profit and Loss

CAT Functions, Graphs and Statistics

CAT Percentages

CAT Time Speed Distance

CAT Time And Work

CAT Geometry

CAT Venn Diagrams

CAT Coordinate Geometry

CAT Remainders

CAT Number Systems

CAT Simple Interest Compound Interest

CAT Arithmetic

CAT Averages

CAT Progressions and Series

CAT Profit And Loss

CAT Number Series

CAT Time, Speed and Distance

CAT Mensuration

CAT Linear Equations

CAT Algebra

CAT Probability, Combinatorics

CAT Logarithms, Surds and Indices

CAT Averages, Ratio and Proportion

CAT Averages Mixtures Alligations

CAT Data Sufficiency