Question: 3. Define the function f: N - N by the following rule: n f ( n ) = 2 , if n is even 3n

3. Define the function f: N - N by the following rule: n f ( n ) = 2 , if n is even 3n + 1 , if n is odd a) Complete the (partial) arrow diagram for f. b) Define f* (n) to be the function f composed with itself k times. For example f3 (n) = f (f (f (n)) ) . Compute f5 ( 9 ) . c) Find the minimum value of k such that f* (10) = 1 d) Is f one to one? Justify your claim. e) Is f onto? Justify your claim

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

3. Define a function f: N -> N, where N is the set of nonnegative integers (including 0), as follows: f(0) = 1 and for n 0, f(3n) = f(n) f(3n+1)=0 f(3n+2) = f(n). (Note that f(3n) = f(n) is...

Let , neN, where N = {1, 2, 3, ..} is the set of positive integers. Define a function f: N N by f(x) = x modn [ f(x) = x modn means that f(x) is the remainder when x is divided by n. For example,...

MUST BE CORRECT ANSWERS A small software company has the following simplified cashflow, funded by shareholders' equity of 20,000 and a bank overdraft of 5000: Invoiced money received 2 months after...

an operation that yields a N aN value when neither of its arguments is a N aN, (b) an operation with finite arguments that yields +, (c) an operation with an argument + that yields a finite result....

Sort the following functions from asymptotically smallest to asymptotically largest. That is, the function f (n) and the next function g (n) must always follow that f (n) element O (g(n)). If the two...

XYZ What is the difference between volatile and nonvolatile memory? Is RAM volatile or nonvolatile? Is ROM volatile or nonvolatile? 7.9 Registers perform a very important role in the fetch-execute...

In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...

different databases CST.2008.6.8 (a) Define the idea of a safe query in relational calculus. [2 notations] (b) Assume we have schemas R(A, B) and S(B, C), where r represents the number of tuples in R...

Write 1. a MATLAB function to calculate the coefficients of Hermite interpolating polynomial, H (using divided difference) 2. a MATLAB function to evaluate the Hermite interpolating polynomial. 3. a...

2. [Sequence] Consider a sequence {an}nez+ satisfying the following conditions: a = 1 an = 1+ + for n > 2 and n e Z+ An-1 2.1. [Golden ratio) The above sequence converges to a, how do you derive the...

A steam power plant operates on a reheat-regenerative Rankine cycle with a closed feed water heater. Steam enters the turbine at 12 MPa, 500oC at a rate of 25 kg/s and is condensed in the condenser...

What will be the final temperature of a mixture made from 25.0 g of water at 15.00, 45.0 g of water at 50.00, and 15.0 g of water at 37.0C? * a) 99.32 F b) 37.4 F c) 99.32 K d) 99.32 C

Brief Exercise 7-29 Units to Earn Target Income Chillmax Company plans to sell 3,500 pairs of shoes at $60 each in the coming year. Unit variable cost is $21 (includes direct materials, direct labor,...

IN Additional comments: When it comes to learning something new, we all have preferred ways of learning. For example, while some people may prefer to learn through images and videos, others learn more