CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

The question is about Function of a function. We need to find out the value of function of a function at x = 3. 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 10: x is a real number such that f(x) = \\frac{1}{x}\\) when x > 0 and f(x) = \\frac{1}{x + 1}\\) otherwise. Also fⁿ(x) = f(f^{n - 1} (x)). What is f(3) + f²(-3) + f³(3) + f⁴(-3)?

1. \\frac{-2}{3}\\)
2. \\frac{14}{3}\\)
3. 0
4. 3

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: Substitute x = 3 or x = -3 as appropriate for the function of a function and get the values.

f(x) = \\frac{1}{x}\\) when x > 0; f(x) = \\frac{1}{x + 1}\\) otherwise

f(3) = \\frac{1}{3}\\)
f(-3) = \\frac{-1}{2}\\)
f²(3) = f(f(3) = f(\\frac{1}{3}\\)) = 3
f²(-3) = f(f(-3) = f(\\frac{-1}{2}\\)) = \\frac{1}{(-1/2 + 1)}\\) = 2

f(3) + f²(-3) + f³(3) + f⁴(-3)
= \\frac{1}{3}\\) + f(f¹(-3)) + f(f²(3)) + f(f³(-3))
= \\frac{1}{3}\\) + f(\\frac{-1}{2}\\) + f(3) + f(f(f²(-3)))
= \\frac{1}{3}\\) + 2 + \\frac{1}{3}\\) + f(f(2))
= \\frac{8}{3}\\) + f[\\frac{1}{2}\\)]
= \\frac{8}{3}\\) + 2
= \\frac{14}{3}\\)

The question is "What is f(3) + f²(-3) + f³(3) + f⁴(-3)?"

Hence the answer is " \\frac{14}{3}\\)"

Choice B is the correct answer.