Asked by ZFeniZ
                Find the values of x for which each function is continuous
f(x)={(-2x+1 if x<0),(x^(2)+1 if x>=0):}
            
        f(x)={(-2x+1 if x<0),(x^(2)+1 if x>=0):}
Answers
                    Answered by
            oobleck
            
    since all polynomials are continuous in their domain, all we need to do is check f(0)
limit(x→0<sup>-</sup>) = -2(0)+1 = 1
f(0) = 0^2 + 1 = 1
so f(x) is continuous at x=0, and thus everywhere.
    
limit(x→0<sup>-</sup>) = -2(0)+1 = 1
f(0) = 0^2 + 1 = 1
so f(x) is continuous at x=0, and thus everywhere.
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