Find the domain of the following function. $$ f(x)=\frac{x-7}{x+9} $$

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UpStudy AI · Accepted Answer

1. The function is given by
   $$
   f(x)=\frac{x-7}{x+9}.
   $$
2. A rational function is undefined when its denominator is zero.
3. To find where the denominator is zero, set
   $$
   x + 9 = 0.
   $$
4. Solve for $$x$$:
   $$
   x = -9.
   $$
5. Therefore, the function is undefined at $$x = -9$$.

Thus, the domain of $$ f(x) $$ is all real numbers except $$ x = -9 $$, which can be written as:
$$
\{ x \in \mathbb{R} \mid x \neq -9 \}.
$$
The domain of $$ f(x) = \frac{x-7}{x+9} $$ is all real numbers except $$ x = -9 $$.

Find the domain of the following function.

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