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(a) Having just finished constructing his time machine, Kik has to adjust one last setting before using his machine. He needs to choose 4 chronologies in time, represented by integers p, q, r, s such that p≤q≤r≤s. Any user of the machine will be able to travel from a year in the interval [p..r] to a year in the interval [q..s]. Help Kik analyse the results of his first trial by determining how many distinct functions there are with domain [p..r], and codomain [q..s].

(a) Having just finished constructing his time machine, Kik has to adjust one last setting before using his machine. He needs to choose 4 chronologies in time, represented by integers p, q, r, s such that p≤q≤r≤s. Any user of the machine will be able to travel from a year in the interval [p..r] to a year in the interval [q..s]. Help Kik analyse the results of his first trial by determining how many distinct functions there are with domain [p..r], and codomain [q..s].

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Please do a part only i need it in 30 min plz don't forget to answer in 30 min plz i need perfect answer plz and take a thumb up
(a) Having just finished constructing his time machine, Kik has to adjust one last setting before using his machine. He needs to choose 4 chronologies in time, represented by integers p, q, r, s such that p≤ q ≤r ≤s. Any user of the machine will be able to travel from a year in the interval [p..r] to a year in the interval [q..s]. Help Kik analyse the results of his first trial by determining how many distinct functions there are with domain [p..r], and codomain [q..s]. (b) Kik is not satisfied with the results of the first trial. In order to make improvements, Kik decides to run a second trial focusing on a specific form of functions. He is interested in functions of the form f: [1..n] → [1..2n], where n is a positive integer, such that for all in the domain we have either f(x) < x or f(x) ≥ 2x. How many distinct functions of that form exist? Justify your answer and put it in closed form.
Transcribed Image Text:(a) Having just finished constructing his time machine, Kik has to adjust one last setting before using his machine. He needs to choose 4 chronologies in time, represented by integers p, q, r, s such that p≤ q ≤r ≤s. Any user of the machine will be able to travel from a year in the interval [p..r] to a year in the interval [q..s]. Help Kik analyse the results of his first trial by determining how many distinct functions there are with domain [p..r], and codomain [q..s]. (b) Kik is not satisfied with the results of the first trial. In order to make improvements, Kik decides to run a second trial focusing on a specific form of functions. He is interested in functions of the form f: [1..n] → [1..2n], where n is a positive integer, such that for all in the domain we have either f(x) < x or f(x) ≥ 2x. How many distinct functions of that form exist? Justify your answer and put it in closed form.
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