# How do you find the domain of f @ g given f(x)= sqrt(x-1) and g(x)= 1/(x-7)?

Jun 14, 2018

$x \in \left(7 , 8\right]$

#### Explanation:

$f \left(\frac{1}{x - 7}\right) = \sqrt{\frac{1}{x - 7} - 1}$

$x \ne 7 \mathmr{and} \frac{1}{x - 7} - 1 \ge 0$

$\frac{1 - x + 7}{x - 7} \ge 0$

$\left(x - 7\right) \left(x - 8\right) \le 0$

$7 \le x \le 8$