FUNCTION. Let f(x)=1/(x-4) and g(x)=7/x+4,

Question

find 1) f(g(x)) 2)g(f(x))?

Answer 1

1) Let f(x) = 1/(x - 4) and g(x) = 7/ (x + 4)

     f(g(x)) = f( 7/(x + 4) )                                          [ Since g(x) = 7/ (x + 4) ]

                 = 1/((7/(x + 4)) - 4)                                 [ Since f(x) = 1/(x - 4) ]

                 = 1/[(7 - 4(x + 4)) / (x + 4) ]

                 = 1/ [ (7 - 4x - 16) / (x + 4) ]

                 = (x + 4) / (-4x -9)

                 = -(x + 4) / (4x + 9)

Therefore   f(g(x))  = -(x + 4) / (4x + 9)

             

Answer 2

2) Let f(x) = 1/(x - 4) and g(x) = 7/ (x + 4)

    g(f(x)) = g(1/ (x - 4))                                             [ Since f(x) = 1/(x - 4) ]

               = 7/ [ (1/(x - 4) ) + 4 ]                                [ Since g(x) = 7/ (x + 4) ]

               = 7/ [ (1 + 4(x - 4)) / (x + 4) ]

               = 7(x + 4) / (1 + 4x -16)

               = 7(x + 4) / (4x - 15)

     Therefore g(f(x))   = 7(x + 4) / (4x - 15)