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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

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.