Question

Question #12cba

Answer 1

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]}