Question

Locate the points of discontinuity in the piecewise function shown below.

{-(x+1)²+2 -[infinity] < x < -1
f(x) = { -x+2: -1 ≤ x < 2
{ √x-1 ; 2 ≤ x < [infinity]
A. x=-1 and 2
B. x=2
C. x=-1
D. no points of discontinuty

Answer 1

The points of discontinuity in the given piecewise function are x = -1 and x = 2.

Step-by-step explanation:

The given piecewise function is:

f(x) = {-(x+1)²+2, -∞ < x < -1

-x+2, -1 ≤ x < 2

√x-1, 2 ≤ x < ∞

To find the points of discontinuity, we look for values of x where the function changes its rules or formulas. In this case, we need to check the values of x at -1 and 2.

At x = -1, the function changes from -(x+1)²+2 to -x+2. This is a point of discontinuity because there is a sudden jump in the values of the function.

At x = 2, the function changes from -x+2 to √x-1. This is also a point of discontinuity because the two formulas have different behaviors at x = 2.

Therefore, the points of discontinuity in the given piecewise function are x = -1 and x = 2.