SOLUTION: Find the domain of the following: g(x)=ln(t+4)

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Question 116014: Find the domain of the following:
g(x)=ln(t+4)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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g%28x%29=ln%28t%2B4%29 Start with the given function

Remember you cannot take the log of a negative value or of zero. So that means the argument t%2B4 must be greater than zero (i.e. the argument must be positive)

t%2B4%3E0 Set the inner expression greater than zero

t%3E0-4Subtract 4 from both sides


t%3E-4 Combine like terms on the right side


So that means t must be greater than -4
So here is the domain in interval notation: (-4,)


Notice if we graph g%28x%29=ln%28t%2B4%29 (just replace t with x), we get
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+ln%28x%2B4%29%29+ notice how the graph never crosses the line x=-4. So this graphically verifies our answer.