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#### Chapter one important questions

10th Standard EM

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Maths

Do not write anything on the question paper
Time : 00:30:00 Hrs
Total Marks : 30

Part - A

15 x 2 = 30
1. 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?

2. If X = {–5,1,3,4} and Y = {a,b,c}, then which of the following relations are functions from X to Y ? R1= {(–5,a), (1,a), (3,b)}

3. Given f(x) =2x-x2, find
(i) f (1)
(ii) f (x+1)
(iii) f (x) + f (1)

4. Find f o g and g o f when f(x)=2x+1 and g(x)=x2-2

5. Represent the function f(x)=$\sqrt { 2x^{ 2 }-5x+3 }$ as a composition of two functions.

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

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

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

9. Find x if gff(x) = fgg(x), given f(x) = 3x+1 and g(x)=x+3.

10. LetA= {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} $\subseteq$ A x B bea relation. Show that R is a function and find its domain, co-domain and the range of R.

11. 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 set of ordered pairs.

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

13. 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 table .

14. 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 .

15. 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.