what is the domain of the function?\nf(x)=\frac{x + 6}{(x - 7)(x + 5)}\na all real numbers except 7\nb all…

Explanation:

Step1: Recall domain - non - zero denominator

The denominator of the function $f(x)=\frac{x + 6}{(x - 7)(x + 5)}$ cannot be zero.

Step2: Set denominator equal to zero

Set $(x - 7)(x + 5)=0$.

Step3: Solve for x

Using the zero - product property, if $(x - 7)(x + 5)=0$, then $x-7 = 0$ or $x + 5=0$. Solving $x-7 = 0$ gives $x=7$, and solving $x + 5=0$ gives $x=-5$.

Answer:

C. all real numbers except $-5$ and $7$