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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.
(1) The following table gives the joint probability distribution p (X, Y) of random variables X and Y. Determine the following: (a) Do the entries of the table satisfy
let X be a nonempty set. let x belong to X. show that the collection l={ union subset of X : union = empty or belong U
Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event B. Likewise for independent
Logarithmic Differentiation : There is one final topic to discuss in this section. Taking derivatives of some complicated functions can be simplified by using logarithms. It i
RATIONAL NUMBERS All numbers of the type p/q where p and q are integer and q ≠0, are known as rational. Thus it can be noticed that every integer is a rational number
Evaluate the perimeter of the plot of land. a. 260 m b. 340 m c. 360 m d. 320 m To evaluate the perimeter, we must know the length of all sides. According to the dia
Coastal Cable had 1,440,000 customers within January of 2002. During the first half of 2002 the company launched a large advertising campaign. Through the end of 2002 they had 1,80
4/x+4-3/x+3=2/x+2-1/x+1
John was doing his homework on vertical addition, and had to compute : 5 3+ 3 4 and 6 8 +45 He did the first one easily, just the way his teacher had taught him. He first ad
2x+4x
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