Q80.Let f and g be two functions defined by f(x) = {x|x+−1|,1, xx≥0< 0 {x1, + 1, xx≥0< 0 (gof)(x) is (1) Continuous everywhere but not differentiable (2) Continuous everywhere but not differentiable at exactly at one point x = 1 (3) Differentiable everywhere (4) Not continuous at x = 1
What This Question Tests
This question tests the continuity and differentiability of a composite function defined piecewise, requiring careful evaluation of limits and derivatives at the critical points.
Concepts Tested
Formulas Used
Left-hand limit
Right-hand limit
Left-hand derivative
Right-hand derivative
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📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Continuity and Differentiability of piecewise functions
- Year
- 2023
- Shift
- 11 Apr Shift 2
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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