Find the domain of the following rational function. g(x)=(-8x^2)/((x-7)(x+2)) Select the correct choice below and, if necessary, fill in the answer A. The domain of g(x) is restricted to square (Type your answer in interval notation. B. The domain of g(x) has no restrictions.

Question

Find the domain of the following rational function. g(x)=(-8x^2)/((x-7)(x+2)) Select the correct choice below and, if necessary, fill in the answer A. The domain of g(x) is restricted to square (Type your answer in interval notation. B. The domain of g(x) has no restrictions.

Answer 1

To find the domain of the rational function \( g(x) = \frac{-8x^2}{(x-7)(x+2)} \), we need to determine where the function is undefined. A rational function is undefined wherever its denominator is equal to zero.The denominator of \( g(x) \) is \((x-7)(x+2)\). We set this equal to zero and solve for

:

This equation is satisfied when either

or

.Solving these equations gives:1.

implies

2.

implies

Thus, the function \( g(x) \) is undefined at

and

.Therefore, the domain of \( g(x) \) excludes these two values. In interval notation, the domain is:

So, the correct choice is:A. The domain of \( g(x) \) is restricted to \( (-\infty, -2) \cup (-2, 7) \cup (7, \infty) \).

Question

Find the domain of the following rational function. g(x)=(-8x^2)/((x-7)(x+2)) Select the correct choice below and, if necessary, fill in the answer A. The domain of g(x) is restricted to square (Type your answer in interval notation. B. The domain of g(x) has no restrictions.

Solution

Resposta