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CBSE CLASS XI

Relations and Functions

Q.1. Define Modulus function.Draw its graph & mapping.What is its domain & range?;

Q.2. Define Signum function.Draw its graph & mapping.What is its domain & range?

Q.3. Let A = {1, 2, 3} B = {3, 4}; ; and C = {4, 5, 6}
Find (A ´ B) Ç (A ´ C).

Q.4. Let A = B = C = D =
Verify A´C is a subset of B´D.

Q.5. If P = { 1,2 }, form the set P x P x P.

Q.6. If f(x) = x3 Find;

Q.7. Let A = {1, 2} and B = { 3, 4}. Find the number of relations from A to B.

Q.8. Let A = {1, 2, 3,...,14}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, where x, y e A}. Write down its domain, co-domain and range.;

Q.9. Find the domain of the function :
(a). f(x) =
(b). f(x) =

Q.10. Find the domain of the following function given by
1 f(x) = x çx ê
2. f(x) =
3. f(x) = [x] + x

Q.11. Find the range of following functions:

(i). 1f(x) =

(ii) 2f(x) =

(iii) nf(x) =

(iv) f(x) = 1 - êx – 2 ç

(v) f(x) =

(vi) f(x) = x2 + 6

(vii) f(x) =

(viii) f(x) =

Q.12. Let f = be a function from R into R. Determine the range of f.

Q.13. The functio n f is defined by : f(x) = Draw the graph of f(x).

Q. 14. Find the domain and range of;; f(x) = .

Q. 15. Draw graph of following functions:

(i) f(x) =

(ii) f(x) = x – [x]

(iii) f(x) = çx -2 ê+ êx - 3ç

(iv) f(x) = { 1, if x £ 0 x2 + 1, if 0 < x < 2

(v) if; x ;2 } 5.f(x) = { 3 – x, if x > 1

(vi) 1, if x = 1

(vii) 2x, if x < 1 }

Q.16. Determine the domain and range of the relation R defined by
R = {(x, x + 5) : x e ;{0, 1, 2, 3, 4, 5}}.

Q.17. Let f(x) = x2 and g(x) = 2x + 1 be two real functions. Find (f – g), .

Q.18. Let f,g : R®R be defined,respectively by f(x) = x + 1,g(x) =2x – 3.Find f + g, .

Q.19. If f(x) = [x] and g(x) = ;where [x] is the greatest integer function and ;is the modulus function then find:.

Q.20. Let f = { (1, 2); (3, 4); (-5, 6) (0, 2) } be a linear function from Z into Z. Find f(x).

Q.21. Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by:
f(x) = ax + b, for some integers a, b. Determine a, b.

Paper By Mr. Anil Kumar Tondak
Email Id : [email protected]
Ph No.: 9811363962