urgent urgent algebra

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find the composite function fog
f(X) = 1/X-5,g(x)-6/x

question 2
find inverse, domain range and asymatotes of each function
f(x)=3+e^4-x
can some one help me please been stuck on these for 2 days need help solving thank you

  • urgent urgent algebra -

    assuming a typo, I see
    f(x) = 1/(x-5)
    g(x) = 6/x

    so, f◦g = f(g) = 1/(g-5)
    = 1/((6/x)-5)
    = 1/((6-5x)/x)
    = x/(6-5x)
    check for some value, say, x=2:
    g(2) = 3
    f(3) = -1/2
    (f◦g)(2)=2/(6-5*2) = 2/-4 = -1/2

    y=3+e^(4-x)
    y-3 = e^(4-x)
    ln(y-3) = 4-x
    x = 4 - ln(y-3)
    so, f^-1(x) = 4 - ln(x-3)

    domain of f is all reals
    range is y>3
    asymptote is y=3

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