Question 1162538
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a)


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \(f\,\circ\,g\)(x)\ =\ f\(g(x)\)\ =\ g(x)\ +\ 2\ =\ 3^x\ +\ 2]


Follow the same procedure to find *[tex \Large \(g\,\circ\,f\)(x)]


b)  Write the two expressions in pencil.  Erase every instance of *[tex \Large x] and write *[tex \Large (3)] in place of every *[tex \Large x].  Do the arithmetic.


c)  Set


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ (g\,\circ\,f\)(x)\ =\ \(f\,\circ\,g\)(x)]


and solve for x.



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3^{x\,+\,2}\ =\ 3^x\ +\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9\cdot{3^x}\ =\ 3^x\ +\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8\cdot{3^x}\ =\ 2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3^x\ =\ \frac{1}{4}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_3(3^x)\ =\ \log_3\(\frac{1}{4}\)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \log_3(1)\ -\ \log_3(4)\ =\ -\log_3(4)\  =\ -\frac{\ln(3)}{\ln(4)}\ \approx\ -1.2619]
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
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