Question

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( y = f(x) ).
( f(x)=ln (x + 5)-4 )
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the domain of ( f ) is
(type your answer in interval notation. use a comma to separate answers as needed.)
b. the domain of ( f ) is empty.

Explanation:

Step1: Determine the domain condition for the logarithmic function

For the function \(y = \ln(u)\), the argument \(u>0\). Here \(u=x + 5\), so we set up the inequality \(x+5>0\).

Step2: Solve the inequality

Subtract 5 from both sides of the inequality \(x+5>0\). We get \(x>- 5\).

Answer:

A. The domain of \(f\) is \((-5,\infty)\)