S.O.S. Mathematics CyberBoard

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

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

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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