Checking continuity at any point
Checking continuity at any point
Last updated at April 16, 2024 by Teachoo
Example 16 Prove that every rational function is continuous.Every Rational function 𝑓(𝑥) is of the form 𝒇(𝒙)= 𝒑(𝒙)/𝒒(𝒙) where 𝑞(𝑥) ≠ 0 & 𝑝, 𝑞 are polynomial functions Since 𝑝(𝑥) & 𝑞(𝑥) are polynomials, and we know that every polynomial function is continuous. Therefore, 𝒑(𝒙) & 𝒒(𝒙) both continuous By Algebra of continuous function If 𝑝, 𝑞 are continuous , then 𝒑/𝒒 is continuous. Thus, Rational Function 𝑓(𝑥)= 𝑝(𝑥)/𝑞(𝑥) is continuous for all real numbers except at points where 𝒒(𝒙) = 0