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 domain of a rational function excludes values that make the denominator zero. Set the denominator equal to zero: $(x - 7)(x + 5)=0$.

Step2: Solve for x

Using the zero - product property, if $ab = 0$, then $a = 0$ or $b = 0$. So $x-7 = 0$ gives $x = 7$ and $x + 5=0$ gives $x=-5$.

Answer:

C. all real numbers except -5 and 7