For each of the following functions, determine whether the function is:• Injective (one-to-one)• Surjective (onto)• BijectiveJustify your answers. a f: ZZ such that f(x) = 4xbf: Z→ Z such that f(x) = x³cf: Z→ Z such that f(x) = [-4]df: R R such that f(x)=3ef: Z+ x Z+ → Z+ such that f(x, y) = 2 + y

a) f:Z→Z, f(x)=4x1.Injective (one-to-one):For f(x1)=f(x2), we must have 4x1=4x2. Dividing by 4 gives…

Answered: For each of the following functions,…

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter13: Overloading And Templates

Section: Chapter Questions

Problem 30SA

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Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.
Prove:Church’s thesis: The class of computable functions is equal to the class of intuitive computable functions.
Which functions are one-to-one? Which functions are onto? Describe the inversefunction for any bijective function.(a) f : Z → N where f is defined by f (x) = x4 + 1(b) f : N → N where f is defined by f (x) = { x/2 if x is even, x + 1 if x is odd}(c) f : N → N where f is defined by f (x) = { x + 1 if x is even, x − 1 if x is odd}
Determine whether each of the following functions f : {a,b,c,d} -> {a,b,c,d} is one-to-one and/or onto. (a) f(a) = b, f(b) = a, f(c) = b, f(d) = c (b) f(a) = b, f(b) = b, f(c) = d, f(d) = c (c) f(a) = b, f(b) = a, f(c) = c, f(d) = d (d) f(a) = d, f(b) = a, f(c) = c, f(d) = b (e) f(a) = c, f(b) = d, f(c) = a
Here are the definitions for functions f and g. f R R defined by f(x) = x2 g: R R defined by g(x) = x3 Answer the following questions 1) is fa 1-1 function? is fa onto function? is f a bijection? Does f have an inverse? If yes, what is the inverse of f? 1) is ga 1-1 function? is g an onto function? is g a bijection? Does g have an inverse? If yes, what is the inverse of g?
how many functions a) map {1,2,3.4.5.6} to {up,down,left,right} b) how many functions in part a are subjective? c) how many have f- inverse(up) =2
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Write T if the sentence is true and F if the sentence is false and correct the false sentence. Answer only 5 of the following The sin() function is a scalar function.
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7. Let P denote the set of all phones in the world such that p ∈ P is a phone. Thus, S(p)denotes that “p is a SamsungTM phone”, N(p) denote that “p is a NokiaTM phone”, and G(p)denote that “p is a GoogleTM phone”. Therefore, express each of the following statements usingquantifiers, logical operations, and the propositional functions: S(p),N(p),G(p).(a) There is a GoogleTM phone that is also a SamsungTM phone.(b) Every NokiaTM phone is a GoogleTM phone.(c) No NokiaTM phone is a GoogleTM phone.(d) Some NokiaTM phones are also SamsungTM phones.(e) Some NokiaTM phones are also GoogleTM phones and some are not. PS: Please do not answer them in a paper format.
Define predefined functions.
pick multiple answers on the second one !

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