Answer:
or
![[0, \infty)](https://img.qammunity.org/2020/formulas/mathematics/high-school/kzgmlket4gqpbbtuuu0w74j1mxojf50vf5.png)
Explanation:
By definition the function
has a domain of
.
Since the function is not defined for the values of x negative or equal to zero.
The range of this function is all the real numbers.
Since
when
and
when
![1\leq x<\infty.](https://img.qammunity.org/2020/formulas/mathematics/middle-school/g8iywy9dk1o9kae7rd25sn2wc787u92vwc.png)
In this case we have the function
![y = log ^ 2 (x-6)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/sk9x44egyxx0sduprcy4tiand74pqj3b37.png)
Therefore since the log function is squared then its range is now
![y\geq 0](https://img.qammunity.org/2020/formulas/mathematics/high-school/o6uwj32i2zfemkw98zlw3h7mw09y1iopnl.png)