Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
Bartleby Related Questions Icon

Related questions

Q: Draw the graph of the function f :R → R defined by f (x) = x3, x∈R.
A: We will make a table for f(x)=x3 x -1 0 1 y -1 0 1
Q: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==
A:
Q: Find the domain and b) Sketch the domain of f(x, y)= In(4x² – y) -5 -2 -1 3 4 5 x
A:
Q: Find and sketch the domain of the function. f(x, y)=√y+√9-x² - y² y
A:
Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.
A:
Q: - Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that…
A:
Q: Find all local extrema of the function f given by f : R? → R, f(x1, r2) = 3x7x2+ x} – 3a? – 3x3 + 2.
A:
Q: Identify an inner function (call it g) of y = (5x + 4)3.Let u = g(x) and express the outer function…
A: y=(5x+4)3
Q: b. Find and sketch the domain of f(x, y, z) = Vz-x² – y²
A: (b) domain of function f(x,y,z) is set of those values of x,y,z where function f(x,y,z) is defined…
Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |
A:
Q: example of two functions t₁ (n) and t₂(n) that satisfy the relations t₁(n) w(n²), t₂(n) = w(n²) and…
A: Given that the two functions t1(n) and t2(n) that satisfy the relations                t1(n)=ω(n2),…
Q: Q1 a) let f be a function defined as f(x)=3x² + 2x². Find f(2), f(-1), f(1). b) Define functions f…
A:
Q: Select the following functions that are bijective. ƒ₂: R → R, ƒ₂(x) = 14 f₂: R → R, f₂(x) = x f₁: R…
A:
Question
**Problem 3:** Determine whether each of these functions is one-to-one/onto. (a) \( f: \mathbb{R} \to \mathbb{R}, \ f(x) = 3x \). (b) \( f: \mathbb{Z} \to \mathbb{Z}, \ f(x) = 5x \). (c) \( f: \mathbb{R} \to \mathbb{Z}, \ f(x) = \lfloor x \rfloor \). **Explanation:** - **(a)** The function \( f(x) = 3x \) maps real numbers to real numbers. To determine if it is one-to-one, check if different inputs result in different outputs: if \( 3x_1 = 3x_2 \), then \( x_1 = x_2 \) (divide both sides by 3). Thus, it is one-to-one. To check if it is onto, consider that for every real number \( y \), there exists an \( x = \frac{y}{3} \) such that \( f(x) = y \). Therefore, it is onto. - **(b)** The function \( f(x) = 5x \) maps integers to integers. It is one-to-one because if \( 5x_1 = 5x_2 \), then \( x_1 = x_2 \). However, it is not onto because not every integer is a multiple of 5. For example, there is no integer \( x \) such that \( f(x) = 1 \). - **(c)** The function \( f(x) = \lfloor x \rfloor \) maps real numbers to integers. This function is not one-to-one, as multiple real numbers can have the same floor value (e.g., \( f(1.2) = 1 \) and \( f(1.9) = 1 \)). It is onto because every integer \( n \) can be represented as \( f(x) \) for \( x \) in the interval \([n, n+1)\).
expand button
Transcribed Image Text:**Problem 3:** Determine whether each of these functions is one-to-one/onto. (a) \( f: \mathbb{R} \to \mathbb{R}, \ f(x) = 3x \). (b) \( f: \mathbb{Z} \to \mathbb{Z}, \ f(x) = 5x \). (c) \( f: \mathbb{R} \to \mathbb{Z}, \ f(x) = \lfloor x \rfloor \). **Explanation:** - **(a)** The function \( f(x) = 3x \) maps real numbers to real numbers. To determine if it is one-to-one, check if different inputs result in different outputs: if \( 3x_1 = 3x_2 \), then \( x_1 = x_2 \) (divide both sides by 3). Thus, it is one-to-one. To check if it is onto, consider that for every real number \( y \), there exists an \( x = \frac{y}{3} \) such that \( f(x) = y \). Therefore, it is onto. - **(b)** The function \( f(x) = 5x \) maps integers to integers. It is one-to-one because if \( 5x_1 = 5x_2 \), then \( x_1 = x_2 \). However, it is not onto because not every integer is a multiple of 5. For example, there is no integer \( x \) such that \( f(x) = 1 \). - **(c)** The function \( f(x) = \lfloor x \rfloor \) maps real numbers to integers. This function is not one-to-one, as multiple real numbers can have the same floor value (e.g., \( f(1.2) = 1 \) and \( f(1.9) = 1 \)). It is onto because every integer \( n \) can be represented as \( f(x) \) for \( x \) in the interval \([n, n+1)\).
Expert Solution
Check Mark
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
bartleby
This is a popular solution
See solutionCheck out a sample Q&A here
Step 1
VIEW
Step 2
VIEW
bartleby

Trending nowThis is a popular solution!

bartleby

Step by stepSolved in 2 steps with 1 images

See solution
Check out a sample Q&A here
Blurred answer
Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Text book image
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Text book image
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Text book image
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Text book image
Basic Technical Mathematics
Advanced Math
ISBN:9780134437705
Author:Washington
Publisher:PEARSON
Text book image
Topology
Advanced Math
ISBN:9780134689517
Author:Munkres, James R.
Publisher:Pearson,
SEE MORE TEXTBOOKS