CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

CAT Questions | Algebra | Functions - Value of a Functions

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, f(2) = 4, find the value of f(4)?

  1. 8
  2. 18
  3. 25
  4. 28

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

Taking x = 4,
\\frac{f(4)}{f(3)}\\) = \\frac{(2)}{(5)}\\)
=> f(5) = f(2) * \\frac{(3)}{(4)}\\)

Putting f(5) in equation (1),
We get (f(4))2 = f(2)f(6) = 81 * 4
f(4) = 9 * 2 = 18

The question is "f(x) is a positive-valued function and f(6) = 81, f(2) = 4, find the value of f(4)?"

Hence the answer is "18"

Choice B is the correct answer.


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