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In this Class 12 Mathematics topic from Continuity and Differentiability, students study functions in which the variable appears in the exponent, such as a^x for a positive base a. They learn their basic properties, domain, range, graphs, growth and decay behaviour, and the role of the number e. The topic also builds understanding of continuity and derivatives of exponential functions, helping students analyse change and solve related calculus problems accurately.
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Medium · Level 7 · sets,union,intervals,endpoint inclusion,Exponential functions,Continuity and Differentiability,Mathematics,Class 12 MCQView options
(0, 4)
(0, 4]
[0, 4)
(0, 2] ∪ (2, 4)
Question 1MediumLevel 7
If A = (0, 2] and B = [2, 4), what is A ∪ B?
Correct answer: A
A contains numbers greater than 0 and up to and including 2. B contains numbers from 2 inclusive up to, but not including, 4. Because 2 is included in both intervals, there is no gap between them. Their union therefore contains every real number greater than 0 and less than 4. The endpoints 0 and 4 are excluded, so the result is (0, 4).
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