Question

Find the values of x for which each function is continuous

f(x)={(-2x+1 if x<0),(x^(2)+1 if x>=0):}

Answer 1

since all polynomials are continuous in their domain, all we need to do is check f(0)
limit(x→0^-) = -2(0)+1 = 1
f(0) = 0^2 + 1 = 1
so f(x) is continuous at x=0, and thus everywhere.