NCERT Class 12 · Ch 5 Exercise 5.1 · Q7
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 7
Discuss continuity and find any discontinuities of f(x)=|x|+3 for x≤−3; −2x for −3<x<3; 6x+2 for x≥3.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: x=3 only.
- At −3 both one-sided limits and f(−3) equal 6, so this junction is continuous.
- At 3 the left limit is −6 but the right limit and f(3) are 20. All other points lie on continuous branches.
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