CAT Online Live Classes

Concepts discussed on May 19, 2018

Algebra - Functions

Welcome to the live session of Functions. The concepts and questions discussed on May 19, 2018 during the live session follow the embedded video. The video link next to each concept will take you to the start of the part of the video where that specific concept is discussed. Click the video embedded below to watch the entire session.

Medium Questions

1. f(x) ranges from –5 to 3. What is the broadest possible range of f(|x|) + |f(x)|?

   1. (–5, 6)
   2. (–10, 6)
   3. (–5, 5)
   4. (-5, 8)
   • Video explanation

2. Find the range of 2sinx + 3cosx.

   1. [-3 , 3]
   2. [-5 , 5]
   3. [-√ 13, √ 13]
   4. [-4 , 4]
   • Video explanation

3. How many elements are present in the domain of ^9-xC_x+1?

   1. 5
   2. 6
   3. 4
   4. 7
   • Video explanation

4. g(x) = x² + 6x + 8 is defined for set of real number to set P. If g(x) is an onto function. Find P.

   1. [–1, ∞)
   2. [1, ∞)
   3. [–1,1]
   4. (–∞, ∞)
   • Video explanation

Tough Questions

5. What is the range of f(x) = $\frac{1}{x^2+6x+6}$?

   1. (0,∞)
   2. (- ∞ , 1/3] U [0, ∞)
   3. (- ∞ , 1/3] U (0, ∞)
   4. (- ∞ , 1/3] U (0, 1/3]
   • Video explanation

6. What is the range of the function f(x) = $\frac{1}{x^2 +4x-5}$?

   1. (-∞, (−1)/9 )
   2. (0, ∞)
   3. (-∞, (−1)/9 ] U [0, ∞)
   4. (-∞, (−1)/9 ] U (0, ∞)
   • Video explanation

7. Function f(x) defined from set of real numbers to set P is an onto function. If f(x) = $\frac{1}{x^2+1}$ , find set P. ?

   • Video explanation

8. Range of f(x) = (–4, 5); range f(|x|) = (–3, 4). Which of the following could be the range of g(x) if g(x) = f(|x|) + |f(x)| + |f(|x|)|?

   1. ( –7, 11)
   2. ( –8, 10)
   3. (- 6, 14)
   4. (- 11, 14)
   • Video explanation

9. f(x) = Remainder of division of 100^x by 19, where x is a whole number. How many elements does the range of f(x) contain?

   1. 9
   2. 19
   3. 18
   4. 12
   • Video explanation