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 $(-5,infty)$. (type your answer in interval notation. use a comma to separate answers as needed.) b. the domain of $f$ is empty. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the $x$-intercept(s) of $f$ is $x=square$. (type an exact answer. use a comma to separate answers as needed.) b. the function $f$ has no $x$-intercepts.

Explanation:

Step1: Find the \(x\) - intercept

Set \(y = f(x)=0\), so \(\ln(x + 5)-4=0\).
Add \(4\) to both sides: \(\ln(x + 5)=4\).
Using the property \(y=\ln u\) implies \(u = e^{y}\), we have \(x+5=e^{4}\).
Subtract \(5\) from both sides: \(x=e^{4}-5\).

Answer:

A. The \(x\) - intercept(s) of \(f\) is \(x = e^{4}-5\)