Answer:
[tex]x \ge 5[/tex] and [tex]x \ne -7[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{\sqrt{x - 5}}{x + 7}[/tex]
Required
The domain
Set the denominator to not equal to 0
[tex]x + 7 \ne 0[/tex]
[tex]x \ne -7[/tex]
Also, the expression in roots must be 0 or positive i.e
[tex]x - 5 \ge 0[/tex]
[tex]x \ge 0+5[/tex]
[tex]x \ge 5[/tex]
Hence, the domain is defined for:
[tex]x \ge 5[/tex] and [tex]x \ne -7[/tex]
