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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 2: Q35E (page 154)

If f and $f \circ g$ are onto, does it follow that g is onto? Justify your answer.

Short Answer

Expert verified

No, it doesn’t follow that g is onto.

Step by step solution

Step: 1

For example, suppose that $A = \{a\}, B = \{b, c\} a n d C = \{d\}$ .

Step: 2

Let $g (a) = b, f (b) = d and f (c) = d$ .

Then f and $f \circ g$ are onto, but is not

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Most popular questions from this chapter

Question: Let $f : R \to R$ and $f (x) > 0$ let for all $x \in R$ . Show that f(x) $f (x)$ is strictly increasing if and only if the function $g (x) = 1 / f (x)$ is strictly decreasing.

a) Show that a partial function from A to B can be viewed as a function from A to B $υ$ {u} , where u is not an element of B and

$f^{*} (a) = \{\begin{cases} f (a) if a belongs to the domain of definition of f \\ uiffisundefinedata \end{cases}$

b) Using the construction in (a), find the function f* corresponding to each partial function in exercise 77.

Find the inverse function of $f (x) = x^{3} + 1$

Question: Let$f(x) = ax + b$ and $g(x) = cx + d$ where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that $f \circ g = g \circ f$

Compute each of these double sums

$\begin{aligned} \sum_{i = 1}^{3} \sum_{j = 1}^{2} (i - j) \\ \sum_{i = 0}^{3} \sum_{j = 0}^{2} (3 i + 2 j) \\ \sum_{i = 1}^{3} \sum_{j = 0}^{2} j \\ \sum_{i = 0}^{2} \sum_{j = 0}^{3} i^{2} j^{3} \end{aligned}$

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If f and $f \circ g$ are onto, does it follow that g is onto? Justify your answer.

Short Answer

Step by step solution

Step: 1

Step: 2

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Most popular questions from this chapter

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If f and f∘g are onto, does it follow that g is onto? Justify your answer.

Short Answer

Step by step solution

Step: 1

Step: 2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Statistics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

If f and $f \circ g$ are onto, does it follow that g is onto? Justify your answer.