SOLUTION: I am having problems remembering domains. I need to find the domain of the following: f(t) = log(t-5) Is the domain (-infinity, +infinity)?

Question 132312: I am having problems remembering domains. I need to find the domain of the following:
f(t) = log(t-5)
Is the domain (-infinity, +infinity)?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

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

Set the inner expression greater than zero

Add 5 to both sides

Combine like terms on the right side

So that means t must be greater than in order for t to be in the domain

So the domain in set-builder notation is

So here is the domain in interval notation:

Notice if we graph (just replace t with x), we get
notice how the graph never crosses the line . So this graphically verifies our answer.

and we can see that x must be greater than in order to lie on the graph

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