KANI MATHS 10th MAHS NOTES OF LESSON FEBRUARY WEEK 1

STD                : 10

SUBJECT     : MATHS

TITLE            : REVISION

SUB TITLE   :  CHAPTER -1 (RELATIONS AND FUNCTIONS)

 DATE             : 30.01.2023 to  03..02.2023

கல்வி சார்ந்த தகவல்களுக்கு நமது சமூக வலை தளங்களான

          

 KANI MATHS Educational Group -ல்  இணைந்து கொள்ளலாம்.

2     Two Mark Question :

1.     If A x B = {(3,2), (3,4), (5,2), (5,4)}, then find A and B.

2.    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?

3.    Let 𝑓 be a function from 𝑅 to 𝑅 defined by 𝑓 (𝑥) = 3𝑥 − 5. Find the values of 𝑎 and 𝑏 given  that (𝑎, 4) and (1, 𝑏) belong to 𝑓.

4.    Let 𝐴 = {1, 2, 3, 4} 𝑎𝑛𝑑 𝐵 = 𝑁. Let 𝑓: 𝐴 → 𝐵 be defined by (𝑥) = 𝑥³ then, (i) find the range of 𝑓   (ii) identify the type of function.

5.    Find  k  if   f of(k) = 5 ,  where f (k) = 2k - 1

6.    Let f(𝑥) = 𝑥² − 1. Find (𝑖)𝑓o𝑓   (𝑖𝑖)𝑓𝑜𝑓𝑜𝑓

 Five  Mark Question :

1.                         1.    Let A={ x ∈ N / 1 < x < 4}, B ={ x ∈W | 0 ≤  x < 2} and C={ x ∈ N | x < 3}.

                   then verify that  A x (B U C) = (A x B ) U ( A x C)

2.    Represent the relation  f(x) = {(x, y) / x=2y, x∈{2,3,4,5},y∈{1,2,3,4} by (a) an arrow diagram, (b) a graph and (c) a set in roster form,

3.    Let 𝐴 = {1,2,3,4} 𝑎𝑛𝑑 𝐵 = {2,5,8,11,14} be two sets. Let 𝑓: 𝐴 → 𝐵 be a function given by 𝑓 (𝑥) = 3𝑥 − 1. Represent this function (i) by arrow diagram (ii) in a table form (iii) as a set of ordered pairs (iv) in a graphical form.    

4.      If  f(x) = 2x+3 , g(x) = 1-2x and h(x) = 3x  . Prove that. (𝑓𝑜𝑔)𝑜ℎ =𝑓o(𝑔𝑜ℎ)

5.    If  f(x) = x - 1 , g(x) = 3x +1  and h(x) = 𝑥²  . Show that (𝑓𝑜𝑔)𝑜ℎ =𝑓o(𝑔𝑜ℎ)