Reference no: EM131609
Problem 1. Solve the following functions for x (where x is a real number). Leave your answers in exact form, that is, do not use a calculator, show all working.
![342_Solve the following functions.png](https://www.expertsmind.com/CMSImages/342_Solve%20the%20following%20functions.png)
Problem 2. A manager has determined the cost C, in dollars, for manufacturing is
![954_Solve the following functions1.png](https://www.expertsmind.com/CMSImages/954_Solve%20the%20following%20functions1.png)
for manufacturing, where q is the number of units produced in a given day.
(a) What is the cost of manufacturing before any units are produced?
(b) What is the cost of manufacturing if 1980 units are produced in a given day?
(c) How many units would be produced if the cost of manufacturing is $150 in a given day?
Problem 3. Find all solutions of the following equations in the interval [0, 2π)
![196_Solve the following functions2.png](https://www.expertsmind.com/CMSImages/196_Solve%20the%20following%20functions2.png)
Problem 4. (a) Sketch the graph of the circular function
![2329_Solve the following functions3.png](https://www.expertsmind.com/CMSImages/2329_Solve%20the%20following%20functions3.png)
i. State clearly the amplitude, phase shift, period and the equation of the midline.
ii. Show working for all θ- and y-intercepts for the function y = f(θ).
iii. Show at least two periods for the graph of y = f(θ), and label the axes clearly.
(b) Prove the following identity
![790_Solve the following functions4.png](https://www.expertsmind.com/CMSImages/790_Solve%20the%20following%20functions4.png)
Make sure you show all working and give clear explanations.
Problem 5. Consider the function
![1650_Solve the following functions5.png](https://www.expertsmind.com/CMSImages/1650_Solve%20the%20following%20functions5.png)
which has the graph
![1340_Solve the following functions6.png](https://www.expertsmind.com/CMSImages/1340_Solve%20the%20following%20functions6.png)
(a) Explain why f has no inverse function. You should include an example to support your explanation.
(b) Determine the largest possible domain, which includes x = 1, for f(x) such that the inverse function f-1(x) does exist.
(c) Given your answers in (b) ?nd the inverse function f-1(x). Clearly explain key steps and show all working.
(d) Sketch the graph of y = f(x) for the restricted domain in (b) and y = f-1(x) on the same set of axes. All points of intersection and axes-intercepts should be easily determined from your sketch or clearly labelled. Furthermore axes should be clearly labelled with appropriate scaling.