## Calcmathlete 3 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.

1. abstracted

$g(x)=f(x-4)$Notice that$f(x-4)=\sqrt{9-(x-4)^2}$ Follow so far?

2. RaphaelFilgueiras

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3. Calcmathlete

Oh...so you plugged in f(x - 4) which is formed by plugging in (x - 4) for x in f(x)?

4. abstracted

Yup$g(x)=f(x-4)=\sqrt{9-(x-4^2)}$

5. Calcmathlete

So it would be: $g(x) = \sqrt{-x^2 + 8x - 7}~?$

6. abstracted

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

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

8. abstracted

That's how I would leave it, unless your professor told you otherwise

9. Calcmathlete

Alright. THank you :) Just needed a quick refresher since I forgot how to do these momentarily!

10. abstracted

Np!