Algebra help needed for determining whether two functions are inverse of each other

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For each pair of functions f and g below, find f(g(x)) and g(f(x)).  Then, determine whether f and g are inverse of each other.

Simplify answers as much possible.  Assume that your expressions are defined for all x in the domain of the composition.

A.  f(x)=x-3/2      B.  f(x)=6x

     g(x)2x+3            g(x)=6x

     f(g(x))=               f(g(x))=

     g(f(x))=               g(f(x))=

f and g are inverses of each other                 A     B 

f and g are not inverses of each other          A      B   

Nov 1st, 2015

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The Answers :

A. f(x)=x-3/2                                  B.  f(x)=6x

    g(x)=2x+3                                        g(x)=6x

   f(g(x))= (2x+3) -3/2                           f(g(x))=6(6x)

              = 2x + 3/2                                        = 12x                                

  g(f(x))=  2(x-3/2) + 3                            g(f(x))=6(6x)

           = 2x - 3 + 3                                             = 12x

           = 2x                      

f and g are not inverses of each other       A       B

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Nov 1st, 2015

Thanks but it was wrong

correct answer is:   A.   f(g(x))=x    g(f(x))=x   then,  B.  should be  36x for both

Nov 1st, 2015

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