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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.
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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abstracted
 2 years ago
Best ResponseYou've already chosen the best response.2\[g(x)=f(x4)\]Notice that\[f(x4)=\sqrt{9(x4)^2}\] Follow so far?

RaphaelFilgueiras
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1344985583558:dw

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0Oh...so you plugged in f(x  4) which is formed by plugging in (x  4) for x in f(x)?

abstracted
 2 years ago
Best ResponseYou've already chosen the best response.2Yup\[g(x)=f(x4)=\sqrt{9(x4^2)}\]

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0So it would be: \[g(x) = \sqrt{x^2 + 8x  7}~?\]

abstracted
 2 years ago
Best ResponseYou've already chosen the best response.2Yes you could simplify it further to what you did,. Just another example: If it was \[g(x)=f(x+5x^2)\] Then:\[g(x)=f(x+5x^2)=\sqrt{9(x+5x^2)^2}\]

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0Oh I get it...but for more practical uses, it would be just left as \[g(x) = \sqrt{9  (x  4)^2}~?\]

abstracted
 2 years ago
Best ResponseYou've already chosen the best response.2That's how I would leave it, unless your professor told you otherwise

Calcmathlete
 2 years ago
Best ResponseYou've already chosen the best response.0Alright. THank you :) Just needed a quick refresher since I forgot how to do these momentarily!
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