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 Post subject: college algebra precalculusPosted: Sun, 4 Mar 2012 21:18:32 UTC
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Joined: Sun, 4 Mar 2012 21:03:26 UTC
Posts: 1
I need some help please. write the expression below as a single logarithm. Please show all work. in x-in(x^2-9)+in(x+3).
The other problem is for the given functions f and g, find fog and state the domain of fog. Please show all work. f(x)=8/x+11 g(x)=x^3-5x^2-9x+34

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 Post subject: Re: college algebra precalculusPosted: Sun, 4 Mar 2012 22:13:18 UTC
 Member

Joined: Tue, 20 Oct 2009 18:18:45 UTC
Posts: 33
Location: Lisbon, Portugal
use the propoerties:
ln(a*b)=ln(a)+ln(b)
ln(a/b)=ln(a)-ln(b)
then fatorize x^2 - 9 like squares difference and simplify with x + 3

(fog)(x) = f[g(x)] = 8 / f(x) + 11
D fog(x) = {x| x € Df and f(x) € Dg}
you must find the domain of f and you must get the intersection between the domain of g and the image of f

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 Post subject: Re: college algebra precalculusPosted: Mon, 5 Mar 2012 03:23:44 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12172
Location: Austin, TX
tl190836 wrote:
I need some help please. write the expression below as a single logarithm. Please show all work. in x-in(x^2-9)+in(x+3).
The other problem is for the given functions f and g, find fog and state the domain of fog. Please show all work. f(x)=8/x+11 g(x)=x^3-5x^2-9x+34

The domain of a composition is all values in the domain of the inner function which give you points in the domain of the outer function as outputs.

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