Answer:
B. (1, 0)
Step-by-step explanation:
Given:
The two functions are:
[tex]f(x)=\ln(x)\\g(x)=\ln (x^2)[/tex]
In order to determine the point of intersection of the graphs of the two given functions, we need to equate the functions.
[tex]f(x)=g(x)\\\ln x=\ln x^2[/tex]
Two log functions with same base are equal only if their terms are equal to each other. Therefore,
[tex]x=x^2\\\textrm{Subtracting x from both sides}\\x-x=x^2-x\\x^2-x=0\\x(x-1)=0\\\therefore x=0\ or\ x-1=0\\\therefore x=0\ or\ x=1[/tex]
But a log function is not defined for [tex]x=0[/tex]. Therefore, the value of [tex]x[/tex] is only equal to 1.
Now, the [tex]y[/tex] value can be obtained using any one of the function.
[tex]f(1)=\ln1-0[/tex] ( Since, log 1 = 0)
Therefore, the point of intersection of the functions [tex]f(x)\ and\ g(x)\ is\ (1,0)[/tex].
The correct option is B. (1, 0).
