8. for f(x) = (x² + 5x + 2)/(x + 1), identify the point of discontinuity. a. x = 1 b. x = 2 c. x = 0 d. x = -1

8. for f(x) = (x² + 5x + 2)/(x + 1), identify the point of discontinuity. a. x = 1 b. x = 2 c. x = 0 d. x = -1

8. for f(x) = (x² + 5x + 2)/(x + 1), identify the point of discontinuity. a. x = 1 b. x = 2 c. x = 0 d. x = -1

Answer

Explanation:

Step1: Recall discontinuity condition

A rational - function $y = \frac{g(x)}{h(x)}$ is discontinuous where $h(x)=0$. For $f(x)=\frac{x^{2}+5x + 2}{x + 1}$, set the denominator equal to zero. $x+1 = 0$.

Step2: Solve for x

Subtract 1 from both sides of the equation $x+1 = 0$. $x=-1$.

Answer:

D. $x = - 1$