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#### Relations and Functions Five Marks Questions

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. The arrow diagram shows a relationship between the sets P and Q. Write the relation in (i) Set builder form (ii) Roster form (iii) What is the domain and range of R.

2. Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}  be a function from A to B. Show that f is one – one but not onto function.

3. If A={-2,-1,0,1,2} and f: A ⟶ B is an onto function defined by f(x)=x2+x+1 then find B.

4. If the function f: R⟶ R defined by

(i) f(4)
(ii) f(-2)
(iii) f(4)+2f(1)
(iv) $\frac { f(1)-3f(4) }{ f(-3) }$

5. Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this (i) an one-one function (ii) an onto function, (iii) both oneone and onto function?

6. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

find 2f(-4) + 3f(2)

7. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

f(-7) -f(-3)

8. A functionf: [-7,6) $\rightarrow$ R is defined as follows.

$\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) }$

9. f(x) = (1+ x)
g(x) = (2x-1)
Show that fo(g(x)) = gof(x)

10. Let A = {1, 2, 3, 4, 5}, B = N and f: A $\rightarrow$B be defined by f(x) = x2. Find the range of f. Identify the type of function.