Question #12cba

1 Answer
Jun 5, 2016

The function is defined and continuous on #x>3/2#.

Explanation:

The function #y=ln(x)# is only defined when #x>0#. The function is continuous on its entirety when it is defined.

So, for the function #y=ln(4x-6)#, we know that #4x-6>0#. This can be solved to show that #x>3/2#.

Therefore the function #y=ln(4x-6)# is defined on the interval #x in (3/2,oo)# and is continuous on that entire interval.

The graph of #y=ln(x)#:
graph{ln(x) [-9.1, 36.51, -12.19, 10.63]}

The graph of #y=ln(4x-6)#:
graph{ln(4x-6) [-9.1, 36.51, -12.19, 10.63]}