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Question : 142 of 160
Marks:
+1,
-0
Solution:
Given that
f(x)={| ‌ | ‌ | ‌ if ‌ | x∈R−{−1,−2} |
| −1 | ‌ | ‌ if ‌ | x=−2 |
| 0 | ‌ | ‌ if ‌ | x=−1 |
.Now, we have to check the continuity
at
x=−2,−1at
x=−2‌ LHL ‌‌=‌| (−2−h)+2 |
| (−2−h)2+3(−2−h)+2 |
‌=‌‌=‌=‌=−1 ‌ RHL ‌‌=‌| (−2+h)+2 |
| (−2+h)2+3(−2+h)+2 |
‌=‌‌=‌‌=‌=−1⇒LHL‌=‌ RHL ‌=f(−2)∴ It is continuous at
x=−2Now, check for
x=−1 ‌begin‌aligned‌ LHL ‌‌=‌| (−1−h)+2 |
| (−1−h)2+3(−1−h)+2 |
‌=‌‌=‌=‌=1‌ RHL ‌‌=‌| (−1+h)+2 |
| (−1+h)2+3(−1+h)+2 |
‌=‌‌=‌=1‌⇒‌ LHL ‌=‌ RHL ‌≠f(−1)‌∴‌ It is not continuous at ‌x=−1The required function is continuous in
R−{−1}.
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