# Math 210 Rasmussen College Inverse and Compositions Functions Excercises

Description

Worksheet 5 [pdf, docx] covers Sections 2.3 (part 2), 4.2, and 2.4. Only the subsections in the worksheet are required for the course.
Assignment:

Solve all the 12 exercises on the worksheet on your own paper or by using your favorite software.
The total of 12 exercises will be graded by completion. On top of  that, I will consider 3 among the 12 exercises for correctness. MT 210

1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

Math 210, Concepts from Discrete Mathematics
Worksheet 5
This is a video guideline. Complete all the proposed exercises after watching the videos posted
on D2L.
Section 2.3 part 2
Inverse Functions and Compositions of Functions.
Watch the videos about inverse and composition of functions.
Exercise 1. Read Definitions 9 and 10 and write the definitions of inverse function and
composition of functions.
Exercise 2. Let f: Z → Z be such that f(n) =n+ 2. Is f invertible and if it is, what is its inverse?
Exercise 3. Determine f ◦ g and g ◦ f where f(x) = x2 + 1 and g(x) = x+ 2 are functions from R to R.
Exercise 4. Let f: R × R → R be such that f(x, y) = x+y. Is f invertible and if it is, what is its inverse?
Can we restrict the domain or the codomain of the function f so that f becomes invertible?
What is the inverse in this case?
Section 4.2
Representation of Integers.
Watch the videos about representation of integers.
Exercise 5. Convert each of the following integers into the required expansion. Show some of
(a) 321 into binary
(b) 1023 into octal
(c) (2653)7 into decimal
(d) 456 into ternary
(f) (11110111)2 into base 7
(g) (126727)8 into binary
Algorithms for Integer Operations.
Watch the videos about integer operations.
Exercise 6. Perform the following sums and products. Show your computations.
(a) (110)2 · (101)2
(b) (10110101)2 + (11000111)2
(c) (2112)3 + (12021)3
(d) (112)3 · (210)3
(e) (23)6 · (14)6
(f) (234)6 + (421)6
(g) (1AE)16 ·(BBC)16
(h) (20CBA)16 + (A01)16
Section 2.4
Sequences
Exercise 7.
List the first 10 terms of the sequence an = floor(√n) for n ≥ 1 where floor(x) is the largest
integer less than or equal to the real number x.
Exercise 8. List the first 10 terms of the sequence an = 2an-1 − an-2, with a0 = 0, a1= 1.
Recurrence Relations
Watch the videos about recurrence relations.
Exercise 9. Assume that the population of the world in 2010 was 6.9 billion and is growing at
the rate of 1.1% a year. Set up a recurrence relation for the population of the world n years
after 2010.
Exercise 10. Show that the sequence an= 2n is a solution of the recurrence relation
an= 5an-1 − 6an-2
Summations
Exercise 11. Find the value of the summation
∑ j from 0 to 3 12 · (−3)j
Exercise 12. Find the value of the following sum as a closed formula in terms of n.
∑j from 0 to n (2·3j+ 3·2j)

attachment

Tags:
sequences

discrete mathematics

recurrence relations

one to one function

Representation of Integers

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.

Peter M.
So far so good! It's safe and legit. My paper was finished on time...very excited!
Sean O.N.
Experience was easy, prompt and timely. Awesome first experience with a site like this. Worked out well.Thank you.
Angela M.J.
Good easy. I like the bidding because you can choose the writer and read reviews from other students
Lee Y.
My writer had to change some ideas that she misunderstood. She was really nice and kind.
Kelvin J.
I have used other writing websites and this by far as been way better thus far! =)
Antony B.
I received an, "A". Definitely will reach out to her again and I highly recommend her. Thank you very much.