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Math Help - functions and domains

  1. #1
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    Unhappy functions and domains

    I think I must have missed something along the way. Can someone please explain to me step by step how to solve this?

    f(x)=1/(x-1), g(x)=(x-1)/(x+1). Find fog gof, fof, gog and their domains.

    First of all, I don't think I even grasp the concept of multiplying with x? I'm very confused and need some serious help. I cannot do functions.
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  2. #2
    Moo
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    Quote Originally Posted by sjenkins View Post
    I think I must have missed something along the way. Can someone please explain to me step by step how to solve this?

    f(x)=1/(x-1), g(x)=(x-1)/(x+1). Find fog gof, fof, gog and their domains.

    First of all, I don't think I even grasp the concept of multiplying with x? I'm very confused and need some serious help. I cannot do functions.
    Multiplying with x ?

    fog=f(g(x))

    So consider f(t)=\frac{1}{{\color{red}t}-1} and let t={\color{red}g(x)}

    so it'll be \frac{1}{{\color{red}\tfrac{x-1}{x+1}}-1}

    Then simplify.
    It will be exactly the same reasoning for gof and fof
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  3. #3
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    Moo, you're always here helping me out. Thanks so much!

    Can you tell me how to simplify, that is the step that I think I must have missed years ago. I am just not understanding it.
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  4. #4
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    try this ...

    clear the fraction in the denominator by multiplying numerator and denominator of \frac{1}{\frac{x-1}{x+1}-1} by (x+1), then simplify.

    you should end up with the more simple fraction
    -\frac{x+1}{2}
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