NCERT Class 12 · Ch 5 Exercise 5.1 · Q9
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.1 Question 9
Discuss continuity and find any discontinuities of f(x)=x/|x| for x<0; −1 for x≥0.
💡 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: No discontinuities.
- For x<0, x/|x|=−1. The other branch is also −1.
- Thus f(x)=−1 everywhere, including at 0, and is continuous.
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