Question

Explain why the function is discontinuous at the given number f(x)=1/x 2, a= -2

Answer 1

The function f(x) = 1/x is discontinuous at x = -2 because the function is not defined for x = 0. When x approaches 0 from the left side (x < 0), the function f(x) approaches negative infinity. But when x approaches 0 from the right side (x > 0), the function f(x) approaches positive infinity. Since the left and right limits of the function at x = 0 are not equal, the function is discontinuous at x = -2.

Step-by-step explanation:

The function f(x) = 1/x is discontinuous at x = -2 because the function is not defined for x = 0. When x approaches 0 from the left side (x < 0), the function f(x) approaches negative infinity. But when x approaches 0 from the right side (x > 0), the function f(x) approaches positive infinity. Since the left and right limits of the function at x = 0 are not equal, the function is discontinuous at x = -2.

Answer 2

The function f(x) = 1/x is discontinuous at x = -2 because it does not have a limit at that point.

Step-by-step explanation:

The function f(x) = 1/x is discontinuous at x = -2. A function is said to be discontinuous at a given point if it does not have a limit at that point. In this case, as x approaches -2 from the left, f(x) approaches negative infinity, while as x approaches -2 from the right, f(x) approaches positive infinity.

One way to visualize the behavior of f(x) = 1/x near x = -2 is to look at its graph. At x = -2, there is a vertical asymptote, which means the function approaches infinity as x approaches -2 from either side.

To summarize, the function f(x) = 1/x is discontinuous at x = -2 because it does not have a limit at that point.