Final answer:
The question seeks a specific value of c for a piecewise function, but the expression in the question is unclear. To solve properly, continuity at x = -1 would be ensured by equating the limit of the function as x approaches -1 to cx when x = -1.
Step-by-step explanation:
The question is asking for a value of c for which the function f(x) behaves in a certain way at x = -1, and offering an expression involving x outside of this value. Unfortunately, the expression provided in the question is incomplete and unclear. However, I can explain how to approach a similar problem involving piecewise functions and finding a limit or value that makes the function continuous at a given point.
For a function that is defined piecewise, such as f(x) = { cx, x = -1; 6, x = 1; x² - 1 / (x + 1)(x - 2)² for other values of x }, you would ensure the continuity of f at x = -1 by finding a value of c such that the limit of the function as x approaches -1 matches the value of the function at that point. In this case, c would be found by setting the limit of x² - 1 / (x + 1)(x - 2)² as x approaches -1 equal to cx when x = -1.