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Calcmathlete

  • 2 years ago

GIven that \(f(x) = \sqrt{9 - x^2}\), and that \(g(x) = f(x - 4)\), rewrite g(x) in terms of x. Please tell me how to do it and not just the answer.

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  1. abstracted
    • 2 years ago
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    \[g(x)=f(x-4)\]Notice that\[f(x-4)=\sqrt{9-(x-4)^2}\] Follow so far?

  2. RaphaelFilgueiras
    • 2 years ago
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    |dw:1344985583558:dw|

  3. Calcmathlete
    • 2 years ago
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    Oh...so you plugged in f(x - 4) which is formed by plugging in (x - 4) for x in f(x)?

  4. abstracted
    • 2 years ago
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    Yup\[g(x)=f(x-4)=\sqrt{9-(x-4^2)}\]

  5. Calcmathlete
    • 2 years ago
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    So it would be: \[g(x) = \sqrt{-x^2 + 8x - 7}~?\]

  6. abstracted
    • 2 years ago
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    Yes you could simplify it further to what you did,. Just another example: If it was \[g(x)=f(x+5x^2)\] Then:\[g(x)=f(x+5x^2)=\sqrt{9-(x+5x^2)^2}\]

  7. Calcmathlete
    • 2 years ago
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    Oh I get it...but for more practical uses, it would be just left as \[g(x) = \sqrt{9 - (x - 4)^2}~?\]

  8. abstracted
    • 2 years ago
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    That's how I would leave it, unless your professor told you otherwise

  9. Calcmathlete
    • 2 years ago
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    Alright. THank you :) Just needed a quick refresher since I forgot how to do these momentarily!

  10. abstracted
    • 2 years ago
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    Np!

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