What is the domain of y equals StartFraction x cubed minus 8 over x squared plus x minus 2 EndFraction?
Answer options with 5 options
A.
all real numbers except 2
B.
all real numbers except negative 2 and 1
C.
all real numbers except negative 1 and 2
D.
all real numbers greater than 0
E.
all real numbers greater than 1
The expression in the denominator, x^2 + x - 2, cannot be equal to zero because division by zero is undefined. To find the values of x for which the denominator is equal to zero, we can set x^2 + x - 2 = 0 and solve for x.
Factoring the quadratic equation, we have (x - 1)(x + 2) = 0. Setting each factor equal to zero gives x - 1 = 0 and x + 2 = 0. Solving these equations, we find x = 1 and x = -2.
Therefore, the domain of the function y = (x^3 - 8)/(x^2 + x - 2) is all real numbers except x = -2 and x = 1.
Answer: B. all real numbers except negative 2 and 1