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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
2-16  Calculus – Differentiation and Integration
Figure 2.10
4
2
-2
-4 -3 -2 -1
4 3 2 1
Solution: Since we can draw a horizontal line that passes through two points, it is not one-to-one.
Similarly, we can draw a horizontal line, particularly, through the negative y-axis (this is possible
because the co-domain is the set of all real numbers) that does not intersect the graph at any point.
Hence, f is not onto.
Therefore, the function is not bijective.
Example 2.14 Test if the following graph is bijective.
-
4
-
3
-
2
-
1 1 2 3 4
4
2
-
2
-
4
Figure 2.11
Solution: The given graph passes the horizontal line test because every horizontal line ...
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Publisher Resources

ISBN: 9789353948221