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find the domain of composite function fog

f(x)=x/x-4; g(x)= -1/x

please show work

  • math -

    f(g) = g/(g-4)
    = (-1/x) / (-1/x - 4)
    = (-1)/(-1-4x)
    = 1/(4x+1)

    domain is all reals except x = -1/4, 0

    f(4) is not defined, but g(x) = 4 when x = -1/4.

    unfortunately, g(0) is not defined, so f(g(0)) is also not defined

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