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2. Let a, b e R and let f be the function Z + Z defined by f(z) - ar + b. For which values of a and b is f an onto (surjective) function? For which values of a and b is f a one-to-one (injective) function?

2. Let a, b e R and let f be the function Z + Z defined by f(z) - ar + b. For which values of a and b is f an onto (surjective) function? For which values of a and b is f a one-to-one (injective) function?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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G 46 6:01 0.70 25 KB/s FUnctions-Exercises.docx 1. For the following functions, determine whether they are injective, surjective, or bijective: (a) f:R+R given by z . (b) f:R+ R given by z+z+ |z|. (c) f:Nx N N given by (n, m) + 2n +1 if n is even (d) f:N+ N given by f(n) = 2n if n is odd (e) f:N+Z given by f(n) = (-1)*2n + [(-1)" – 1). 2. Let a, b e R and let f be the function Zz → Z defined by f(z) = ar + b. For which values of a and b is f an onto (surjective) function? For which values of a and b is f a one-to-one (injective) function? 3. Let A and B be finite sets with JA| - m and |B|- n. a) How many functions are there from A to B? b) Suppose that m < n. How many injective functions are there from A to B? How about if m> n? e) Suppose n= 2. How many surjective functions are there from A to B? d) (Harder) Suppose n = 3. How many surjective functions are there from A to B? 4. Let f. g be the functions R+R given by 5- 3z if z< 1 f(z) -1 5-2r - if z> 1, 9) - if z<5 For each of these functions, determine whether they are invertible and if so, find their inverses. 5. Let f and g be the functions R + R given by 5- 3z if z< 1 5- 2r -1 if z>1 f(z) and g(z) – 6 - 2. Calculate fog. gof. Rotate screen Fit screen Enter Browser
Transcribed Image Text:G 46 6:01 0.70 25 KB/s FUnctions-Exercises.docx 1. For the following functions, determine whether they are injective, surjective, or bijective: (a) f:R+R given by z . (b) f:R+ R given by z+z+ |z|. (c) f:Nx N N given by (n, m) + 2n +1 if n is even (d) f:N+ N given by f(n) = 2n if n is odd (e) f:N+Z given by f(n) = (-1)*2n + [(-1)" – 1). 2. Let a, b e R and let f be the function Zz → Z defined by f(z) = ar + b. For which values of a and b is f an onto (surjective) function? For which values of a and b is f a one-to-one (injective) function? 3. Let A and B be finite sets with JA| - m and |B|- n. a) How many functions are there from A to B? b) Suppose that m < n. How many injective functions are there from A to B? How about if m> n? e) Suppose n= 2. How many surjective functions are there from A to B? d) (Harder) Suppose n = 3. How many surjective functions are there from A to B? 4. Let f. g be the functions R+R given by 5- 3z if z< 1 f(z) -1 5-2r - if z> 1, 9) - if z<5 For each of these functions, determine whether they are invertible and if so, find their inverses. 5. Let f and g be the functions R + R given by 5- 3z if z< 1 5- 2r -1 if z>1 f(z) and g(z) – 6 - 2. Calculate fog. gof. Rotate screen Fit screen Enter Browser
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