Find the domain of the rational expression. $$ f(x)=\frac{-1}{x^{2}-2 x-35} $$

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1. The domain of the function $$ f(x)=\frac{-1}{x^{2}-2 x-35} $$ consists of all real numbers $$ x $$ except those that make the denominator equal to zero.

2. To find the values to exclude, we solve the quadratic equation:
   $$
   x^{2}-2x-35=0
   $$

3. Factor the quadratic expression:
   $$
   x^{2}-2x-35 = (x-7)(x+5)
   $$

4. Set each factor equal to zero and solve for $$ x $$:
   $$
   x-7=0 \quad \Rightarrow \quad x=7
   $$
   $$
   x+5=0 \quad \Rightarrow \quad x=-5
   $$

5. These two solutions, $$ x=7 $$ and $$ x=-5 $$, are the values that make the denominator zero. Therefore, they must be excluded from the domain.

6. The domain of $$ f(x) $$ is all real numbers except $$ x=7 $$ and $$ x=-5 $$. In set notation, the domain is:
   $$
   \{ x \in \mathbb{R} : x \neq -5 \text{ and } x \neq 7 \}
   $$
The domain of $$ f(x) $$ is all real numbers except $$ x = -5 $$ and $$ x = 7 $$.

Find the domain of the rational expression. \( f(x)=\frac{-1}{x^{2}-2 x-35} \)

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