Algebra

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Help please! I got so far with this and stopped because of confusion. Here is what I have so far.

Let f(x) = 6/x-1 and g(x) = 1 + 3/x find the composite function of (fog)(x)

(fog)(x) = f (g(x))

=f (1+3/x)

=6/x-1

????

  • Algebra -

    ok up to
    =f (1+3/x) , then
    = 6/[1+3/x - 1]
    = 6/(3/x)
    = 2x

  • Algebra -

    So 2x would be the answer? I was thinking about including the 1+3/x-1 in the middle of the problem... So then 2x is it then I suppose?

  • Algebra -

    It is a good idea to check you final answer by picking some value of x

    e.g let x = 3
    g(3) = 1+3/3 = 2
    then f(g(3)) = f(2) = 6/(2-1) = 6

    my expression was f(g(x)) = 2x
    then f(g(3)) = 2(3) = 6

    Even though this does not "prove" that I have the right answer, there is a very high probability that it is correct.

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