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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.
Higher Order Derivatives : Let's begin this section with the given function. f ( x ) = 5x 3 - 3x 2 + 10 x - 5 By this point we have to be a
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Minimum and Maximum Values : Several applications in this chapter will revolve around minimum & maximum values of a function. Whereas we can all visualize the minimum & maximum v
advantages and disadvantages of index numbers
Q UADRATIC EQUATIONS: For the things of this world cannot be made known without a knowledge of mathematics. Solve by factorization a. 4x 2 - 4a 2 x +
( 1/2)2 x 1/5+1/6=
Indeterminate forms Limits we specified methods for dealing with the following limits. In the first limit if we plugged in x = 4 we would get 0/0 & in the second limit
Find the 35th term of the sequence in which a1 = -10 and the common difference is 4.
Heaviside or step function limit : Calculates the value of the following limit. Solution This function is frequently called either the Heaviside or step function. We
HOW MUCH WILL A NEW CAR COST? THE AVERAGE COST OF A NEW CAR IN 1990 WAS $14371. IN 2003 THE AVERAGE COST HAD RISEN TO $22360. WHAT IS THE AMOUNT OF THE MONTHLY PAYMENT? THE AMOUNT
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