Examine the following functions for continuity :
f(×)=×2−25×+5,x×not=−5
f(×)=×2−25×+5=(×+5)(×−5)(×+5)=×−5
∴f(×)=×−5 is a polynomial function, so f(x) is continuous at all values of x.
Note In any rational function f(x)=p(x)q(x) and if P(x) and q(x) are polynomials and q(x) is zero at any value of x and p(x) = 0, then f(x) is not continuous at that point.