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CBSE CLASS XII

Functions and Relations (4/6 Mark)

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41. If find f(f(x))
42. Solve for x:
43. If show that f(f(x)) is an identity function.
44. Show that the relation R in the set A= {x ε Z ; 0 ≤ x ≤ 12} given by R = { ( a,b) : |a-b| is multiple of 4}is an equivalence relation . Also find the set of all elements related to 4.
45. Check whether the relation R defined in the set {1,2,3,4,5,6} as R = { (a,b): b = a +1} is reflexive, symmetric or transitive.
46. Let A = {-1,0,1,2}, B = [ -4,-2,0,2} and f , g : A →B be the function defined by f(x) = x² – x , x ε A and g(x) = 2| x - 1/2 | , x ε A ; are f and g equal. Justify your answer.
47. Show that f [ 1, -1 ] →R given by f(x) = x/x+2 is one-one. Find the inverse of function. f: [ -1 ,1] & Range (f).
48. Express in the simplest form.
49. Let given by f(x)= x| x |is a bijection
50. If f, g : R → Rare defined respectively by Find
    i) fog
    ii) gof
    iii) fof
    iv) gog
51. Let f, g : R → R be two functions such that Find f(x) and g(x).
52. Consider f, g : N → N and h : N → Rdefined as f(x) = 2x, g(y)= 3y+4, and h(z)= Sin z for all x,y,z ε NShow that ho(gof) = (hog)of
53. Let and . Find
    
    
    
54. Let is a bijection

Submitted By Mrs. E.Praveen
Email Id : [email protected]