# CAT Online Live Classes

Algebra - Functions

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

1. [-3 , 3]
2. [-5 , 5]
3. [-√ 13, √ 13]
4. [-4 , 4]
3. How many elements are present in the domain of 9-xCx+1?

1. 5
2. 6
3. 4
4. 7
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. (–∞, ∞)
5. #### Tough Questions

6. 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]
7. 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, ∞)
8. 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. ?

9. 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)
10. f(x) = Remainder of division of 100x 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