Reference no: EM131082259
Functions worksheet - Math 1A, section 106
1. If f(x) = 2x, what is f(2)?
2. How is the graph of y = 2 sin x+ 1 related to the graph of y = sin x? Sketch the graph of the former.
3. How is the graph of y = √x related to the graph of y = √(x - 1)? Sketch the graph of the former and find its domain.
4. If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 7, find a function f such that f o g = h.
5. If f(x) = 3x + 5 and h(x) = 3x2 + 3x + 2, find a function g such that f o g = h.
6. Find the inverse of the function f(x) = 3x + 5. What is f-1 o h where h(x) = 3x2 + 3x + 2 as above? How does this relate to the answer to the previous problem?
7. Find the inverse of the function f(x) = 2 · 3x/4. What is the domain of the inverse function?
8. Find the inverse of the function f(x) = 2x2, which is defined on the domain x ≤ 0.
9. What is the domain of the function f(x) = log2(log3(x))? What is its range? Is it one-to-one? If so, what is its inverse?
10. Does the function f(x) = x4 + 2x2 + 1, defined on R, have an inverse? If so, what is its inverse?
11. Find the inverse f-1 of the function f(x) = 3x + 5, and compute f-1 o f and f o f-1. What do you get in either case? Is there a general principle here?
12. Johnny has a play-doh collection, and each year he decides to use his allowance to buy half as much play-doh as he currently has and add to his collection. If he started with three pounds of play-doh when he was 5 years old, approximately how much play-doh will he have when he is 10 years old, to the nearest pound? (You may use a calculator to find an approximate answer.)
13. In music, why do we have a twelve tone scale?
(a) It is known that simple ratios of frequencies sound nice together to our ears. For instance, when we move up an octave in pitch from the middle C on a piano to the C above, the sound wave doubles in frequency. To move up to the G above middle C, the frequency is multiplied by 1.5. If the frequency of middle C is 261.6, what is the frequency of the C above that? Of the G just above it?
(b) On a piano, there are seven half-steps from the C to the G above it. Use a calculator to compute 27/12. What is it close to?
(c) Given this, what do you think happens to the frequency when we move up a half step on a piano?
14. A confused cell with a terrifying genetic mutation divides into two cells exactly one minute after being created. Then, after another minute each of the two new cells will divide, and so on. Furthermore, at any moment in time that some cells undergo a division, three extra cells with the same terrifying genetic mutation are brought forth from the Void. So, at time t = 0 there is 1 cell, at t = 1 minute there are 2 + 3 = 5 cells, and at time t = 2 minutes there are 2 · 5 + 3 = 13 cells. Find a formula for the number of cells as a function of time in minutes.
Evaluate the given limit
: Quiz 2 - Math 1A, section 106. Evaluate the following limit, if it exists. limt→0(1/t - 1/t2+t)
|
What is the equivalent uniform annual cost
: The initial cost of a piece of equipment is $10,000, and it has a salvage value at the end of its 10 year life of $1,000. Maintenance cost is estimated to be $500 the first year and increase $50 per year to the end of its 10 year life. If the company..
|
Compute the net present worth to determine whether
: A machine costs $1,000,000 to purchase and will produce $200,000 per year revenue. Annual operating and maintenance cost is $50,000. The company plans to use the machine for 10 years and then sell it for scrap for which it expects to receive $50,000...
|
Company must receive each year to breakeven on investment
: A company purchases a new unit of machinery for $20,000. The machinery is to be sold at the end of 10 years for $2,000.If the company uses a MARR of 10%, what is the equivalent uniform net profit cash flow the company must receive each year to breake..
|
Find a formula for the number of cells as a function of time
: Functions worksheet. A confused cell with a terrifying genetic mutation divides into two cells exactly one minute after being created. Then, after another minute each of the two new cells will divide, and so on. Find a formula for the number of cel..
|
Main components of financial analysis
: What are the main components of ‘Financial Analysis' while working out the Detail Project Report? Why ‘Margin Money' for working capital is required to be provided as ‘Initial Investment' for the first year of operation?
|
Extract these location coordinates from this html file
: Complete the exercise by reading the plain text in your character vector into a data frame. Use read table () to do this. The parameters, text, skip, header, and sep should be useful here.
|
Question regarding the chicago manual style
: Sociologist argue that the individual must first learn society's culture in order to effectively interact with those around him/her. to What extent to you agree to this statement.
|
What interest rate must the investment earn
: A teacher invests $5,000 at the end of every year for a 30-year career.If this teacher wants to have $1,000,000 in savings at retirement, what interest rate must the investment earn? (Show Work)
|