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Maths XII

 DATE OF SUBMISSION.25. 6.2013

1. Let f :N® R be afunction defined by f(x) =4x2+ 12x+ 15. Show that f; N ® S,  whereS                         the range of f, is invertible and find f -1.

2.If f(x) = x+7 and  g(x) =x-7,  xÎ R.Find (f0g)(7)

3. Let A be the set of real numbers except -1 and a mapping *  fromAXA to A  be defined    by a* b = a+b+ab  for all a,b ÎA.

  Prove that  1       *.is a binary operation

1)            * is commutative

2)             find the identity element

3)             find the invertible elements and their inverses

 

 4) Let* be  a binary operation   defined by  a*  b  =3ab/ 5. Show that *  is commutative   and assosiative.Find the identity element, if exists.

 5)Let  f: I ® N defined by  f(m)   =   2m  ,m>0

                                                             1-2m ,m≤ 0.  Is f  1-1.one to one  ,onto,invertible. 

 6) Evaluate  cos( sin -1 1/Ö2 + cos-1 1/Ö2).

 7)Find  x  if  sin -1 (5/x)+ sin-1(12/x) = p/2

 8) Show that sin -1 (4/5) + sin -1 (5/13) + sin -1 (16/65)  =p/2

 9) Prove that tan -11  + tan -1 2  + tan -1 3  = 0

10)If sin-1 x +sin -1y  = p/2.  Find cos -1 x  + cos -1 y

11) Find  tan -1 (Ö3)  + sec -1 (-2)

12)Evaluate cot -1 (Ö 1+cos x  + Ö1-cos x   / Ö1+cos x  Ö1-cos x).

Mr Sreekumar R, PGT (Maths)

      


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