CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

The question is about Value of a Functions. We need to find out the value of the function for x = 4. 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 22: If \\frac{f(x)}{f(x-1)}\\) = \\frac{(x-2)}{(x+1)}\\), for all x ≥ 0 and f(x) is a positive-valued function and f(6) = 81, find the value of f(4)?

1. 8
2. 283.5
3. 25
4. 28

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: How we would find out the value when only some details are given?

Taking x = 6,
\\frac{f(6)}{f(5)}\\) = \\frac{(4)}{(7)}\\) ……………(1)

Taking x = 5,
\\frac{f(5)}{f(4)}\\) = \\frac{(3)}{(6)}\\) = \\frac{(1)}{(2)}\\) ……………(2)

Putting equation (2) in equation (1),
We get f(4) = f(6) * \\frac{(7)}{(2)}\\)
f(4) = 81 * \\frac{(7)}{(2)}\\) = 283.5

The question is "f(x) is a positive-valued function and f(6) = 81, find the value of f(4)?"

Hence the answer is "283.5"

Choice B is the correct answer.