domain of f(x)=(sqrt(x+5))/(x-8)

We save the definition:

f (x) = \frac{\sqrt{x + 5}}{x - 8}

1) Let's evaluate the domain of

\frac{\sqrt{x + 5}}{x - 8}

For the expression

\frac{\sqrt{x + 5}}{x - 8}

to be defined, we must have:

x - 8 \neq 0

For the expression

\sqrt{x + 5}

to exist, you must check:

x + 5 \geq 0

2) Let's solve in

ℝ

x - 8 \neq 0

ⓘ We add

8

to both sides

Solution obtained:

x \neq 8

3) Let's solve in

ℝ

x + 5 \geq 0

ⓘ We subtract

5

from both sides

Solution found:

x \geq -5

Let's create the table of the different solutions to find the overall solution:

▶Domain of definition:

x \in [-5, 8) \cup (8, +∞)