Question

What are the domain restrictions of the expression g²+7g+12/g²−2g−24 ? Select each correct answer.

O g≠−6
O g≠4
O g≠3
O g≠6
O g≠−3
O g≠−4

Answer 1

The domain restrictions for the expression g²+7g+12/g²−2g−24 are g≠4 and g≠-6.

Step-by-step explanation:

The domain restrictions of the expression g²+7g+12/g²−2g−24 are values of g that make the denominator equal to zero, since division by zero is undefined in mathematics. To find these restrictions, we set the denominator g²−2g−24 equal to zero and solve for g. Factoring the quadratic expression, we get (g−4)(g+6)=0 which gives us the solutions g=4 and g=-6. Therefore, the domain restrictions for the expression are g≠4 and g≠-6.

The expression is given as: g²+7g+12/g²−2g−24. To find the domain restrictions, we need to consider the values of g for which the denominator is not equal to zero because division by zero is undefined. So, set the denominator equal to zero and solve for g. The factorization of g²−2g−24 = (g−6)(g+4) gives us the values g=6 and g=-4. Therefore, the correct domain restrictions are g≠6 and g≠-4.