what is the domain of the piecewise function

f(x)={2x^2 -2,if x < or= 1 {x+1,if x>1?

To determine the domain of a piecewise function, we need to consider the values of x for which each segment is defined.

In this case, we have two segments:

1. The first segment, 2x^2 - 2, is defined for all x values less than or equal to 1. So, the domain for this segment is (-∞, 1].

2. The second segment, x + 1, is defined for all x values greater than 1. So, the domain for this segment is (1, +∞).

To find the overall domain of the piecewise function, we take the intersection of the domains of each segment. In this case, the intersection is at x = 1.

Therefore, the domain of the piecewise function f(x) = {2x^2 - 2, if x ≤ 1; x + 1, if x > 1} is (-∞, 1] U (1, +∞).