Question

Compare the domains of the logarithmic function f(x) and the square root function g(x).

Graph of f(x):
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/al2_9_20a_media02.gif
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/img_alg02u09c03q25d_02.gif
In two or more complete sentences, explain whether or not the domains of the two functions are the same.

Answer 1

We have that the logarithmic function has a domain from 0 (without including 0) to plus infinity. That is because of the property that e=2.71 raised to any power is positive. We also have that the square root function is defined only from 0 to plus infinity, since every square of a number is positve or 0. The answer is that the domains differ; they are almost equal, except for the fact that the domain of the square root function additionally contains 0.