Exercise: Relation and Function

UNIT EXERCISE

1. If the ordered pairs (x2  − 3x, y2  + 4y) and (-2, 5) are equal, then find x and y.

2. The cartesian product A×A has 9 elements among which (–1, 0) and (0,1) are found. Find the set A and the remaining elements of A×A

3. Given that f (x) = 

(i) f (0)

(ii) f (3)

(iii) f (a + 1) in terms of a.(Given that a ≥ 0 )

4. Let A = {9,10,11,12,13,14,15,16,17} and let f: A → N be defined by f (n) = the highest prime factor of n ∈ A . Write f as a set of ordered pairs and find the range of f.

5. Find the domain of the function f (x) = 

6. If f (x) = x2 , g(x) = 3x and h(x) = x − 2 , Prove that (f o g) o h = f o (g o h)

7. Let A = {1, 2} and B = {1, 2, 3, 4} , C  = {5, 6} and D = {5, 6, 7, 8} . Verify whether A×C is a subset of B×D?

8. If  f (x) = [x-1]/[x+1], x ¹ 1 show that f (f (x)) = −1/x provided x ≠ 0

9. The functions f and g are defined by f (x) = 6x + 8; g(x) = [x-2]/3

(i). Calculate the value of gg(1/2)

(ii) Write an expression for gf (x) in its simplest form.

10. Write the domain of the following real functions

(iv) h(x) = x + 6

Answers:

1. 1,2 and -5 ,1

2. {-1, 0, 1} , {(- 1, -1),(- 1, 1),(0, -1),(0, 0),(1, -1),(1, 0),(1, 1)}

3.(i) 4 (ii) √2 (iii) √a

4. {(9, 3),(10, 5),(11, 11),(12, 3),(13, 13),(14, 7),(15, 5),(16, 2),(17, 17)} , {2,3,5,11,13,17}

5. {–1,0,1}

9.(i) -5/6 (ii) 2(x + 1)

10.(i) R - {9} (ii) R (iii) [2, ∞) (iv) R