Join WhatsApp Icon CAT WhatsApp Group
Instructions

Directions for the following two questions:

Answer the questions on the basis of the information given below.

$$f_1(x) = x$$ if $$0 \leq x \leq 1$$ $$f_1(x) = 1$$ if x >= 1 $$f_1(x) = 0$$ otherwise

$$f_2(x) = f_1(-x)$$ for all x

$$f_3(x) = -f_2(x)$$ for all x

$$f_4(x) = f_3(-x)$$ for all x

Question 4

How many of the following products are necessarily zero for every x:

$$f_1(x)f_2(x), f_2(x)f_3(x), f_2(x)f_4(x)$$

Solution

Share

Checking for different values of x . Suppose x= -0.5 we get

$$f_1(x)f_2(x) = 0*0.5 = 0$$

$$f_2(x)f_4(x) = 0.5*0 = 0$$ .

But $$f_2(x)f_3(x)$$ is not equal to zero.

Hence two functions are necessarily equal to zero and two products given above are equal to zero.

Was this solution helpful?

Get AI Help

Video Solution

video
View More Questions From Functions, Graphs and Statistics

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 41+ 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 Logarithms, Surds and Indices QuestionsCAT Probability, Combinatorics QuestionsCAT Data Sufficiency QuestionsCAT Logarithms QuestionsCAT Progressions and Series Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Truth Lie Concept QuestionsCAT Maxima-Minima QuestionsCAT 2D & 3D LR QuestionsCAT Miscellaneous LR QuestionsCAT Coins and Weights Questions

CAT Verbal Ability Questions | VARC Questions For CAT

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

Free CAT Quant Questions

CAT Logarithms, Surds and IndicesCAT LogarithmsCAT Number SystemsCAT Averages Mixtures AlligationsCAT Profit And LossCAT GeometryCAT Averages, Ratio and ProportionCAT Venn DiagramsCAT Probability, CombinatoricsCAT InequalitiesCAT PercentagesCAT Data SufficiencyCAT MiscellaneousCAT Functions, Graphs and StatisticsCAT Linear EquationsCAT Profit and LossCAT Simple Interest Compound InterestCAT Time And WorkCAT RemaindersCAT Time Speed DistanceCAT AveragesCAT Progressions and SeriesCAT MensurationCAT Time, Speed and DistanceCAT ArithmeticCAT Coordinate GeometryCAT Quadratic EquationsCAT Number SeriesCAT Algebra

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Start your IIM journey with the right preparation and crack CAT 2026.

Enroll Now
Ask AI