6. Determine the domain and range of each of the following functions and whether they are...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
6. Determine the domain and range of each of the following functions and whether they are one-to-one or onto: (a) f- ((r, 9) €N x Ny = 2r + 3} (b) f= {(1, v) EN x Ny=-4} (c) f= ((r, y) €Zx Z|y--3} 10, 00) and let f be a subset of D x R defined by f= {(r, y) : =y+1). Is f a 7. Let D = real-valued function with domain D? 8. Find the domain and range of each function: (a) /: 10,1)- -R defined by f(z) = (b) f(-) = (e) f: Z R defined by f(r) = |r|.- 9. Let f: R-R be defined by f(r) =1+r. (a) Prove that / is bijective. (b) Find f and verify that fof= l=fof. 10. Show whether or not the function is invertible. If yes, find its inverse. (a) f:RR if defined by f(r) = -1. (b) f: (0, )R if defined by f(r) =-1 (c) f: (-0,0) – -Rif defined by f(x) =- 1. (d) f(z) = defined on its domain. %3D (e) S(r) = V-z defined on its domain. 11. Let f: N-Z be defined by S(2) = +2 and g: N-Z be defined by g(n) =2 n. (a) Determine whether fog is well defined; that is, whether the range of the function g is a subset of the domain of the function f. If it is well defined, write a formula for (fog)(2) explicitely. (b) Determine whether gof is well defined; that is, whether the range of the function f is a subset of the domain of the function g. If it is well defined, write a formula for (go )(x) explicitely. 12. Let /: (1, o) R be defined by f(r)-- 2r+1. (a) Show that f in 1-1, or give a counterexample. (b) Show that / is onto, or give a counterexample. 13. Let /:N- Z be defined lay flr) =-1. (a) Show that /is 1-1, or give a counterexample. (b) Show that / ls onto, or give a counterexample. 14. (a) Let f:D Aand g: A C. Prove that if gof: D l is onto then g is onto (b) Asnume noow that :D- A and g: A C. Prove that if gof: D Cin one-to-one then fin one-to-on. 6. Determine the domain and range of each of the following functions and whether they are one-to-one or onto: (a) f- ((r, 9) €N x Ny = 2r + 3} (b) f= {(1, v) EN x Ny=-4} (c) f= ((r, y) €Zx Z|y--3} 10, 00) and let f be a subset of D x R defined by f= {(r, y) : =y+1). Is f a 7. Let D = real-valued function with domain D? 8. Find the domain and range of each function: (a) /: 10,1)- -R defined by f(z) = (b) f(-) = (e) f: Z R defined by f(r) = |r|.- 9. Let f: R-R be defined by f(r) =1+r. (a) Prove that / is bijective. (b) Find f and verify that fof= l=fof. 10. Show whether or not the function is invertible. If yes, find its inverse. (a) f:RR if defined by f(r) = -1. (b) f: (0, )R if defined by f(r) =-1 (c) f: (-0,0) – -Rif defined by f(x) =- 1. (d) f(z) = defined on its domain. %3D (e) S(r) = V-z defined on its domain. 11. Let f: N-Z be defined by S(2) = +2 and g: N-Z be defined by g(n) =2 n. (a) Determine whether fog is well defined; that is, whether the range of the function g is a subset of the domain of the function f. If it is well defined, write a formula for (fog)(2) explicitely. (b) Determine whether gof is well defined; that is, whether the range of the function f is a subset of the domain of the function g. If it is well defined, write a formula for (go )(x) explicitely. 12. Let /: (1, o) R be defined by f(r)-- 2r+1. (a) Show that f in 1-1, or give a counterexample. (b) Show that / is onto, or give a counterexample. 13. Let /:N- Z be defined lay flr) =-1. (a) Show that /is 1-1, or give a counterexample. (b) Show that / ls onto, or give a counterexample. 14. (a) Let f:D Aand g: A C. Prove that if gof: D l is onto then g is onto (b) Asnume noow that :D- A and g: A C. Prove that if gof: D Cin one-to-one then fin one-to-on.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Determine the kernel and range of each of the following linear operators on P3. (a) L(p(x)) = xp'(x) (b) L(p(x)) = p(x) - p'(x) (c) L(p(x)) = p(0)x + p(1)
-
Determine the domain and range of the function f : {r, s, t , u} {A,B,C,D,E} defined by f (r) = A, f (s) = B, f (t) = B, f (u) = E.
-
State the domain and range of each of the functions in Problems. 1. y = x2 + 4 2. y = x2 - 1 3. y = (x + 4 4. y = (x2 + 1
-
The top ten fiction books on The New York Times Best Sellers List on October 9, 2016, are listed. 1. The Girl on the Train 2. Home 3. The Kept Woman 4. Magic Binds 5. Commonwealth 6. The Light...
-
What are the long-term consequences for Doles decision not to focus primarily on taste?
-
Explain which of the three products shown in is formed when 1-butene reacts with HCI.
-
Algonquin Equipment reported the following items on November 30, 2010 (amounts in thousands, with last years amounts also given as needed): Requirements 1. Compute Algonquin Equipments (a) quick...
-
Evan Neal operates a roller skating center. He has just received the monthly bank statement at January 31 from Citizen National Bank, and the statement shows an ending balance of $575. Listed on the...
-
Suggest any FIVE (5) strategies to overcome the reported Justice Theory, Deontology, and utilitarianism in the context of business ethics.
-
On January 2, 2020, Brook Company acquired machinery by issuing a 3%, $360,000 note due in five years on December 31, 2024. Annual payments are $78,608 each December 31. The payment schedule is:...
-
Write a summary of the Commerce Clause and its affect on business activity. Also include a discussion of the power of the states to regulate commerce and the so-called balancing test regarding such...
-
In Groups of 2 answer the 2 below questions. This should be completed on a word document and submitted by email. This assignment is worth 10% of your final grade. You will need to back each...
-
Consider the importance of aviation maintenance technicians during the inspection process, how electrical schematics are used in troubleshooting and repairing aircraft electrical systems, and how...
-
Discuss the various incentives and mechanisms of earnings management in firms. Your discussion should provide a comprehensive definition of earnings management. How may earnings management behaviour...
-
Discuss specifically the corporate governance Strengths, Weaknesses, Opportunities, and Threats (SWOT) of ORACLE CORPORATION. Explain in detail! how some of the observations you have made relate to...
-
Company X is an online pharmacy. Recently, colleagues used a computer program to analyze the purchasing behavior of customers sorted by ZIP code and found that customers in some ZIP codes are, on...
-
Solve for r. 1.32 58.05= r-0.1 Enter your response rounded to 4 DECIMAL PLACES Number
-
Use the following data to answer the next two (2) questions: Product 1 Product 2 Product 3 Direct Material Cost $25,000 $30,000 $35,000 Direct Labor Cost $30,000 $40,000 $50,000 Direct Labor Hours...
-
Describe the set as a union of finite or infinite intervals. {x : |x - 4| > 2}
-
In Exercises 3-10, determine whether the series converges absolutely, conditionally, or not at all. 1. 2. 1 n1/3 (-1)n-1 (LI)n
-
The volume (in liters) and pressure P (in atmospheres) of a certain gas satisfy PV = 24. A measurement yields V = 4 with a possible error of 0.3 L. Compute P and estimate the maximum error in this...
-
Hydrogen gas is expanded reversibly and adiabatically from a volume of \(2.12 \mathrm{dm}^{3}\) at a pressure of \(4 \mathrm{~atm}\) and \(32^{\circ} \mathrm{C}\) until the volume is doubled....
-
If \(C_{P}=a+b T+C T^{2}\), derive a relation to the isobaric mean heat capacity \(\dot{Q}\).
-
A spherical balloon of 1 m diameter contains a gas at 120 kPa. The gas inside the balloon is heated until the pressure reaches 360 kPa. During heating the pressure of the gas inside the balloon is...
Study smarter with the SolutionInn App