Continuity of a piecewise funct​​ion Let g(x) = <matrix 2x1> For what values of a is g continuous?

Verified step by step guidance

1. Identify the piecewise function g(x) and determine the points where the function changes definition, which are typically the boundaries of the pieces.
2. For each piece of the function, ensure that the limits from the left and right at the boundary points are equal to the function value at that point.
3. Set up the equations based on the continuity condition: the limit as x approaches the boundary from the left must equal the limit as x approaches from the right, and both must equal g at that boundary.
4. Solve the resulting equations for the variable 'a' to find the values that ensure continuity at the boundary points.
5. Verify that the values of 'a' found maintain continuity across all relevant points in the piecewise function.