# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Functions Questions | Question 31

The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for Free) head out here: CAT Official Question Mocks. In CAT 2017 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank

Question 31 : If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is [TITA]

## Best CAT Coaching in Chennai

### Explanatory Answer

##### Method of solving this CAT Question from Functions

Given that f(ab) = f(a) × f(b) for all possible integers a and b.
We have to find the largest possible value of f(1). We know that,
f(ab) = f(a) × f(b)
⟹ f(a × 1) = f(a) × f(1)
⟹ [f(a) × f(1)] – f(a) = 0
⟹ f(a)[f(1) – 1] = 0
There are two possibilities here, either f(a) = 0 or f(1) – 1 = 0.
If f(a) = 0, then it is a constant function. Hence, f(1) = 0.
But, if f(1) – 1 = 0, f(1) = 1.
Hence, f(1) = 0 or f(1) = 1.
Out of these, f(1) = 1 is the largest possible value.

The question is "If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is [TITA]"

##### Hence, the answer is 1

###### 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

##### 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
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com