CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

The question is about Composite Function. Given the relations between two functions we need to find out the option which is correct. 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 18: If f(x) = \\frac{1}{g(x)}\\), then which of the following is correct?

1. f(f(g(g(f(x))))) = g(f(g(g(g(x)))))
2. f(f(f(g(g(g(f(g(x)))))))) = g(g(g(g(f(g(f(f(x))))))))
3. f(f(g(f(x)))) = g(g(f(g(x))))
4. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: Comparing composite functions.

Given, f(x) = \\frac{1}{g(x)}\\) => f(x).g(x) = 1 which implies that f(x) and g(x) are essentially inverse of one another.
So, one just has to look for an option which has equal number of fs and gs on both side of the equation.

The question is "If f(x) = \\frac{1}{g(x)}\\), then which of the given is correct?"

Hence the answer is "f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))"

Choice D is the correct answer.