Example 12 - Chapter 5 Class 12 Continuity and Differentiability

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Example 12 Discuss the continuity of the function defined by π(π₯)={β(& π₯+2, ππ π₯<0@&βπ₯+2, ππ π₯>0)β€
π(π₯)={β(& π₯+2, ππ π₯<0@&βπ₯+2, ππ π₯>0)β€
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
β΄ f(x) is continuous for x < 0
Case 2 : When x > 0
For x > 0,
f(x) = βx + 2
Since this a polynomial
It is continuous
β΄ f(x) is continuous for x > 0
Hence, π is continuous for all Real points except 0.
Thus, π is continuous for π βπβ{π}

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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