Example 12 - Discuss continuity of f(x) = {x + 2, -x + 2

Example 12 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Example 12 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Concept wise

Transcript

Example 12 Discuss the continuity of the function defined by 𝑓(π‘₯)={β–ˆ(& π‘₯+2, 𝑖𝑓 π‘₯<0@&βˆ’π‘₯+2, 𝑖𝑓 π‘₯>0)─ 𝑓(π‘₯)={β–ˆ(& π‘₯+2, 𝑖𝑓 π‘₯<0@&βˆ’π‘₯+2, 𝑖𝑓 π‘₯>0)─ Here, function is not defined for x = 0 So, we do not check continuity there We check continuity for different values of x When x < 0 When x > 0 Case 1 : When x < 0 For x < 0, f(x) = x + 2 Since this a polynomial It is continuous ∴ f(x) is continuous for x < 0 Case 2 : When x > 0 For x > 0, f(x) = βˆ’x + 2 Since this a polynomial It is continuous ∴ f(x) is continuous for x > 0 Hence, 𝑓 is continuous for all Real points except 0. Thus, 𝒇 is continuous for 𝒙 βˆˆπ‘βˆ’{𝟎}

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.