domain of f(x)=7/x*9/(x+9) — step-by-step solution

We save the definition:

f (x) = \frac{7}{x} \cdot \frac{9}{x + 9}

1) Let's find the domain of

\frac{7}{x} \cdot \frac{9}{x + 9}

For the expression

\frac{7}{x}

to be defined, we must have:

x \neq 0

For the expression

\frac{9}{x + 9}

to be defined, we must have:

x + 9 \neq 0

Solution obtained:

x \neq 0

2) Let's solve in

ℝ

x + 9 \neq 0

ⓘ We subtract

9

from both sides

Solution obtained:

x \neq -9

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

▶Domain of definition:

x \in ℝ \ {-9, 0}