Join WhatsApp Icon CAT WhatsApp Group
Question 59

Let r be a real number and $$f(x) = \begin{cases}2x -r & ifx \geq r\\ r &ifx < r\end{cases}$$. Then, the equation $$f(x) = f(f(x))$$ holds for all real values of $$x$$ where

Solution
Share

When x< r

f(x) = r

f(x) = f(f(x))

r = f(r)

r= 2r-r

r=r

When x>=r

f(x) = 2x-r

f(x) = f(f(x))

2x-r = f(2x-r)

2x-r = 2(2x-r) - r

2x-r = 4x-3r

or, x=r

Therefore x<= r

video
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 Profit And Loss QuestionsCAT Venn Diagrams QuestionsCAT Averages QuestionsCAT Probability, Combinatorics QuestionsCAT Arithmetic Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Games and Tournamnents QuestionsCAT Table based DI Sets QuestionsCAT Scheduling QuestionsCAT Data Interpretation Basics QuestionsCAT 2D & 3D LR Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Vocabulary QuestionsCAT Grammar and Sentence Correction QuestionsCAT Critical Reasoning QuestionsCAT Reading Comprehension QuestionsCAT Para Summary Questions

Free CAT Quant Questions

CAT Time, Speed and Distance

CAT Algebra

CAT Mensuration

CAT Simple Interest Compound Interest

CAT Profit and Loss

CAT Data Sufficiency

CAT Quadratic Equations

CAT Averages

CAT Time Speed Distance

CAT Number Series

CAT Venn Diagrams

CAT Linear Equations

CAT Time And Work

CAT Logarithms, Surds and Indices

CAT Arithmetic

CAT Averages, Ratio and Proportion

CAT Profit And Loss

CAT Coordinate Geometry

CAT Inequalities

CAT Logarithms

CAT Percentages

CAT Geometry

CAT Progressions and Series

CAT Averages Mixtures Alligations

CAT Number Systems

CAT Probability, Combinatorics

CAT Functions, Graphs and Statistics

CAT Remainders