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anonymous
 one year ago
f(x)= x7/x+2 g(x)=2x7/x3 find f(g(x)) and g(f(x))
anonymous
 one year ago
f(x)= x7/x+2 g(x)=2x7/x3 find f(g(x)) and g(f(x))

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0G(x)= 2x7/x1 (correction)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0prepare to do a raft of algebra

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x)=\frac{x7}{x+2}\\ g(x)=\frac{2x7}{x1}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok lets to \[f(g(x))\] first

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what i am going to do is use cut and paste to put \[\frac{2x7}{x1}\] everywhere i see an \(x\) in \[\frac{x7}{x+2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large f(g(x))=f(\frac{2x7}{x1})=\frac{\frac{2x7}{x1}7}{\frac{2x7}{x1}+2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0clear what i did? that is the first step, bunch of algebra comes next

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes I understand so far :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now before we do the algebra, i want to let you know that a miracle will occur the reason you were given this problem is that \(f\) is the inverse of \(g\) and vice versa that means when we get done we will find \[f(g(x))=x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0staring here \[\frac{\frac{2x7}{x1}7}{\frac{2x7}{x1}+2}\] get rid of the compound fraction by multiplying top and bottom by \(x1\) (carefully)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{2x77(x1)}{2x7+2(x1)}\] is step one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0notice the judicious use of parentheses

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now remove the parentheses using the distributive property to get \[\frac{2x77x+7}{2x7+2x2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0combine like terms, and since they are inverses you will get an orgy of cancellation \[\frac{9x}{9}=x\]finished

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0method for doing the second one is similar

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am a bit confused for the second one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0same as the first, only inside out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I put..g(f(x))= 2(x7/x+2)7/(x7/x+2)1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0try it and see what happens it will be easy enough to know if you are right or not, because the answer will be \(x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah that looks right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0However after this step I wasn't positive if I should multiply both by x+2 or distribute

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes multiply top and bottom by \(x+2\) like i did before, carefully, using parentheses

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think I'm doing this correctly ::
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