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Consider the function
f(x) =1/2 (2x +2-x)
which has the graph
(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) find 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. It is suggested you use different colours for the two graphs and clearly label each graph.
All numbers refer to exercises (and not "computer exercises") in Gallian. §22: 8, 16, 22, 24, 28, 36. In addition: Problem 1: Let a be a complex root of the polynomial x 6 +
I am learning this at school today and I started getting confused which one is which, can you help me?
An investment manager at TD Ameritrade is making a decision about a $10,000,000 investment. There are four portfolio options available and she is looking at annual return of these
Following is some more common functions that are "nice enough". Polynomials are nice enough for all x's. If f ( x) = p ( x ) /q (x ) then f(x) will be nice enough provid
Write 3.5 × 104 in decimal notation? Move the decimal point 4 places to the right to get 35,000.
1/2+1/2
Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example Graph y = - 2/5 x + 3 .
let R be a (noncommutative) ring. Given that a,b and a+b ? R are all units, prove that a^(-1)+b^(-1) is a unit
1. Consider the following context free grammar G with start symbol S (we write E for the empty string, epsilon): S ---> bB | aSS A ---> aB | bAA B ---> E | bA | aS a. D
At a bakery the cost of 30 experts is 45$. Write an equation that shows the cost of 45 cookies
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