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

what is the domain of the function?\n\n$f(x)=\\frac{x + 6}{(x - 7)(x + 5)}$\n\na all real numbers except 7\n\nb all real numbers except 5 and -7\n\nc all real numbers except -5 and 7\n\nd all real numbers

what is the domain of the function?\n\n$f(x)=\\frac{x + 6}{(x - 7)(x + 5)}$\n\na all real numbers except 7\n\nb all real numbers except 5 and -7\n\nc all real numbers except -5 and 7\n\nd all real numbers

Answer

Explanation:

Step1: Determine the denominator

For a rational function ( f(x)=\frac{x + 6}{(x - 7)(x + 5)} ), the denominator is ( (x - 7)(x + 5) ).

Step2: Find when the denominator is zero

Set ( (x - 7)(x + 5)=0 ). Using the zero - product property: If ( x-7 = 0 ), then ( x = 7 ); If ( x + 5=0 ), then ( x=-5 ).

Step3: State the domain

The domain of a rational function is all real numbers except the values of ( x ) that make the denominator zero.

Answer:

C. all real numbers except ( - 5) and (7)