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#### Relations and Functions Two Marks Question

10th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. If A x B = {(3,2), (3,4), (5,2), (5,4)} then find A and B.

2. Let A = {x $\in$ N| 1 < x < 4}, B={x $\in$ W| 0 ≤ x < 2) and C={x $\in$ N| x < 3} Then verify that
(i) A x (B U C) = (A x B) U (A x C)
(ii) A x (B ∩ C) = (A x B) ∩ (A x C)

3. Let X={1,2,3,4} and Y={2,4,6,8,10} and R={(1,2),(2,4),(3,6),(4,8)} Show that R is a function and find its domain, co-domain and range?

4. A relation ‘f’ is defined by f(x)=x2-2 where x$\in${-2,-1,0,3}
(i) List the elements of f
(ii) Is f a function?

5. If f(x)=3x-2, g(x)=2x+k and if f o g = f o f, then find the value of k..

6. Find k if f o g(k) = 5 where f(k)=2k-1.

7. If f(x)=2x+3, g(x)=1-2x and h(x)=3x. Prove that f 0 (f o g) o h.

8. State whether the graph represent a function. Use vertical line test.

9. Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

10. Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Letf: A $\rightarrow$B be a function given by  f(x) = 2x + 1. Represent this function as a graph.