1. Chapter 5 Class 12 Continuity and Differentiability
2. Serial order wise

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Example 20 Show that the function f defined by f (x) = |1β π₯ + | π₯ ||, where x is any real number is a continuous πο·π₯ο·― = ο·1βπ₯+ο·π₯ο·―ο·― Let π(π₯) = 1βπ₯+ο·π₯ο·― & β(π₯) = ο·π₯ο·― Then ο·β π πο·―ο·π₯ο·― = βο·πο·π₯ο·―ο·― = βο·1βπ₯+ο·π₯ο·―ο·― = ο·1βπ₯+ο·π₯ο·―ο·― Now β(π₯) = ο·π₯ο·― We know that Modulus function is continuous β β(π₯) = ο·π₯ο·― is continuous π(π₯) = ο·1βπ₯ο·―+ο·π₯ο·― Since ο·1βπ₯ο·― is a polynomial & we know that every polynomial function is continuous β ο·1βπ₯ο·― is continuous & β(π₯) = ο·π₯ο·― is also continuous We know that Sum of two continuous function is also continuous πο·π₯ο·― = 1βπ₯+ο·π₯ο·― is continuous . Hence πο·π₯ο·― & βο·π₯ο·― are both continuous . If two function of πο·π₯ο·― & βο·π₯ο·― both continuous then their composition ο·β π πο·―ο·π₯ο·― is also continuous Hence πο·πο·― is continuous .