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anonymous

  • one year ago

Express the following function, F(x) as a composition of two functions f and g. f(x)= x^2/(x^2+4) @misty1212

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  1. misty1212
    • one year ago
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    you have many choices here, but the easiest one is probably \(g(x)=x^2\) and \(f(x)=\frac{x}{x+4}\)

  2. misty1212
    • one year ago
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    then if you compose them you get \[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\]

  3. anonymous
    • one year ago
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    wait can you show me how you got that?

  4. misty1212
    • one year ago
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    how i got which part?

  5. anonymous
    • one year ago
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    the answer

  6. misty1212
    • one year ago
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    \[f(g(x))=f(x^2)=\frac{x^2}{x^2+4}\] this?

  7. anonymous
    • one year ago
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    yes

  8. misty1212
    • one year ago
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    that is how you compose functions if \(g(x)=x^2\) then \[f(g(x))=f(x^2)\]

  9. misty1212
    • one year ago
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    this is kind of a crappy explanation, lets see if i can do better

  10. anonymous
    • one year ago
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    I'm a bit confused....which is the answer?

  11. misty1212
    • one year ago
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    \[f(g(x))=\frac{x^2}{x^2+4}\] is the question your job is to come up with an \(f\) and a \(g\) that work

  12. misty1212
    • one year ago
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    when you see \(\frac{x^2}{x^2+4}\) the first thing you notice is that the variable is squared top and bottom right?

  13. anonymous
    • one year ago
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    right

  14. misty1212
    • one year ago
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    that is why i picked the "inside function " \(g(x)\) as \(g(x)=x^2\)

  15. misty1212
    • one year ago
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    then the outside part, since we already know the variable is going to be square, looks something like \[f(\spadesuit)=\frac{\spadesuit}{\spadesuit+4}\]

  16. misty1212
    • one year ago
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    if you replace \(\spadesuit\) by \(x^2\) you get what you want\[\frac{x^2}{x^2+4}\]

  17. misty1212
    • one year ago
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    so make the inside function \(g(x)=x^2\) and the outside function \(f(x)=\frac{x}{x+4}\) that way you get what you want when you compose them

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