find the domain

ln(x) does not have real values when \(\displaystyle x\leq 0\)

Therefore, solve \(\displaystyle x+4 > 0\) to find the domain.
 
Find domain of g(x)=ln(x+4)
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The domain is the allowable x values. A good way to determine this is to look at a graph of the function. Please graph this on a calculator or by hand to see what I mean.

The “parent” function of the one you have given is simply f(x) = ln(x). This logarithmic function has the y-axis as an asymptote. The function has no values to the left of the y-axis. Therefore, the domain would be from 0 to infinity, with 0 being excluded. One type of notation to show this is (0, infinity).

In the problem you have stated, “x” has been replaced with “x+4”. What does this do to the graph/function? It slides (translates) the function 4 units to the left.

This means that the asymptote, which used to be on the y-axis (x=0), has also shifted 4 units to the left. The asymptote is now x = -4. The domain is now (-4, infinity).

Make sense?
 
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