# CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

###### CAT Questions | Algebra | Functions - Value of a Functions CAT 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, f(2) = 4, find the value of f(4)?

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

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##### 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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