summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of (…
summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( f(x)=lnleft(x^{2}+36\right) ).\nfind the domain. select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the domain is all real ( x ), except ( x= )\n(use a comma to separate answers as needed.)\nb. the domain is all real numbers.\nfind the ( x )-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( x )-intercept(s) is (are) ( x= )\n(round to one decimal place as needed. use a comma to separate answers as needed.)\nb. there are no ( x )-intercepts.
Answer
Explanation:
Step1: Find the domain
For the function (y = \ln(u)), the argument (u=x^{2}+36) must satisfy (u>0). Since (x^{2}\geqslant0) for all real (x), then (x^{2}+36\geqslant36>0) for all real (x).
Step2: Find the (x -) intercept
The (x -) intercepts occur when (y = f(x)=0). Set (\ln(x^{2}+36)=0). Using the property (\ln a = b\Leftrightarrow a = e^{b}), we have (x^{2}+36=e^{0}=1). Then (x^{2}=1 - 36=- 35). Since (x^{2}=-35) has no real solutions (because the square of a real number (x), (x^{2}\geqslant0) for all real (x)).
Answer:
For the domain: B. The domain is all real numbers. For the (x -) intercept: B. There are no (x -) intercepts.