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Math Help - [SOLVED] Find the domain of the composite function

  1. #1
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    Question [SOLVED] Find the domain of the composite function

    Instructions: Find the domain of the composite function f (of) g.

    f(x)= (-45)/(x) g(x)=(-7)/(x-9)
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    Question And Another Composite Function...

    Here's another one.

    Instructions: For the given functions f and g, find the requested composite function.

    find (g (of) f) (x)

    f(x)=(x-10)/(7) g(x)=7x+10

    Here's what I got...I basically just want to check my answer:

    g(f(x))= 7((x-10)/(7))+10

    g(f(x))=x-10+10

    g(f(x))=x
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  3. #3
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    Quote Originally Posted by GeminiAngel619 View Post
    Instructions: Find the domain of the composite function f (of) g.

    f(x)= (-45)/(x) g(x)=(-7)/(x-9)
    You can study some online lessons to learn how to get started on finding the domain of a function.

    Since, in your case, you are finding f(g(x)), you will need to find the restrictions on the domains of each of f and g (which you'll find by checking for division-by-zero problems), and also you'll need to figure out the x-value for g which gives an output that would be a problem for f.

    (Hint: Since you can't divide by zero, and since f(0) would create a division by zero, then you'll need to find what x-value(s), if any, would cause g(x) to equal zero.)

    Quote Originally Posted by GeminiAngel619 View Post
    Instructions: For the given functions f and g, find the requested composite function.

    find (g (of) f) (x)

    f(x)=(x-10)/(7) g(x)=7x+10

    Here's what I got...I basically just want to check my answer:

    g(f(x))= 7((x-10)/(7))+10

    g(f(x))=x-10+10

    g(f(x))=x
    Your work looks good to me!
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  4. #4
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    Quote Originally Posted by stapel View Post
    You can study some online lessons to learn how to get started on finding the domain of a function.

    Since, in your case, you are finding f(g(x)), you will need to find the restrictions on the domains of each of f and g (which you'll find by checking for division-by-zero problems), and also you'll need to figure out the x-value for g which gives an output that would be a problem for f.

    (Hint: Since you can't divide by zero, and since f(0) would create a division by zero, then you'll need to find what x-value(s), if any, would cause g(x) to equal zero.)


    Your work looks good to me!
    Right, I understand how to do it, on most other problems. And I know that I need to find g(x)=0 (right?) to find out what x-values, if any, would cause the function to equal zero. But when I do that, all I get is -7=0, which is not true/undefined/whatever you want to say.

    Here's how I got -7=0:

    (-7)/(x-9)=0

    multiply both sides by common denom. (x-9)

    and you get (-7)=0.

    This is where I'm stuck.
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  5. #5
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    So in other words...

    The restrictions on the domain are x cannot equal 9 or 0. I understand that part. Its the next step that I'm not doing so hot on. lol
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  6. #6
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    Quote Originally Posted by GeminiAngel619 View Post
    Right, I understand how to do it, on most other problems. And I know that I need to find g(x)=0 (right?) to find out what x-values, if any, would cause the function to equal zero. But when I do that, all I get is -7=0, which is not true/undefined/whatever you want to say.
    What does that tell you? Can g(x) ever be zero? Think about it.

    find (g (of) f) (x)

    f(x)=(x-10)/(7) g(x)=7x+10

    Here's what I got...I basically just want to check my answer:

    g(f(x))= 7((x-10)/(7))+10

    g(f(x))=x-10+10

    g(f(x))=x
    Correct. You would get the same thing with (f\circ g)(x) (but that doesn't always happen). We say that f and g are inverses of each other, because they "undo" each other, so to speak.
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