Maths Assignment Xii

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Maths assignment XII
RELATIONS AND FUNCTIONS 1. If fx= x and x= x , then evaluate fog52-gof-72. 2. If fx= 3-x313 and x= logex , find fof(x). 3. Let * be a binary operation defined by a*b = 2ab – 7. Is * associative? 4. Let A={1,2,3} and ={4,5,6} , f:A→B is a function defined on f1=4 , f2= 5 and f3=6. Write the inverse of f as a set of ordered pairs. 5. Let ‘*’ be a binary operation defined on the set Z as a a*b = a+b+1 for a,b ∈ I. find the identity element. 6. If fx=x-1x+1 ;x≠-1 , then find f-1x. 7. Show that the signum function given by fx=1, if x is greater than 0, if x=0, -1 , if x is less than 0 is neither one-to-one nor onto. 8. If f:R→R, a,b,c,d ∈ R such that ( a,b ) * ( c,d ) = (ac, b+ad ). Find the identity element. 9. Give an example for a relation which is neither reflexive nor symmetric. 10. Consider f,g :N →N and h : N →R defined as fx=2x , gy=3y+4 , and hz=sinz for all x,y,z ∈ N. Show that ho(gof) = (hog)of. 11. Let A = R X R and let * be a binary operation on A defined by ( a,b )*( c,d ) = ( ad+bc , bd ) for all ( a,b ) , ( c,d ) ∈ R X R. Determine if * is commutative , associative , has identity and inverse. 12. Let A = {-1 , 0 , 1 , 2 } , B = [ -4 , -2 , 0 , 2 } and f,g :A→B be the function defined by fx=x2-x, x∈A and gx=2x-12-1 , x∈A ; are f and g equal ? Justify your answer. 13. If fx=5x+34x-5, show that f(f(x)) is an identity function. 14. Let fx=x and gx= x. Find (i) gof-53-(fog)-53 (ii) gof53-(fog)53 (iii) f+2g-1 15. 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

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