Question

let be the function()=3−1 4−1for <−1for −1≤≤12for >12 find the values of and that make the function continuous.

Answer 1

The values of α and β are determined by ensuring that the left-hand and right-hand limits at the boundaries of the piecewise function f(x) are equal, making the function continuous.

Step-by-step explanation:

To ensure that the function f(x) is continuous, we need to find the values of a and b that make the function f(x) seamless at its piecewise boundaries, which are at x = -1 and x = 12. Continuity at a point requires that the left-hand limit equals the right-hand limit, and these both equal the function's value at that point.

For continuity at x = -1:

These two expressions must equal the same value for the function to be continuous at x = -1.

For continuity at x = 12:

These expressions must equal for the function to be continuous at x = 12. In summary, the values for α and β can be found by solving the equations created from setting the two expressions on either side of the piecewise boundaries to equal one another.