By Gareth J. Janacek & Mark Lemmon Close

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Of these, a total of 35 people experienced third degree burns, and 25 experienced both third degree burns and nausea. How many subjects experienced nausea? 3. A total of 1055 0 MSc degrees were earned in 2002. Out of the 41 MSc degrees in music and music therapy, 5 were earned by men. Men earned 650 MSc degrees. How many women earned MSc degrees in fields other than music and music therapy? 4. A survey of 200 credit card customers revealed that 98 of them have a Visa account, 113 of them have a Master Card, 62 of them have a Visa account and a American Express, 36 of them have a Master Card account and an American Express, 47 of them have only a Master Card account, 32 have a Visa account and a Master Card account and an American Express.

It is these technical issues we look at next. The set X is called the domain of the function f and Y is codomain. We are normally more interested in the set of values { f (x) : x E X}. This is the range R sometimes called the image of the function. 1 Examples We can have f ;X^Y where 1. f (x) = 2X where X = {x ; 0 < x < oo} and Y = {y ; 0 < x < oo} 2. f (x) = ^fx where X = {x ; 0 < x < oo} and Y = {y ; 0 < y < oo} 3. f (x) = s i r r 1 (x) where X = {x ; -n/2 < x < pi/2} and Y = {-1 < y < 1} If we think of the possibilities we have • There may be some points in Y (the codomain) which cannot be reached by function f.

C) How many serve breakfast, but neither have full table service, nor serve beer? (d) How many serve beer and have full table service? 6. When | x |< 1 then show that • 1/(1 -x) = 1 + x + x2 + xs + x4-\ 1/(1 _ x ) V 2 = ! + hx^H (1/2)x+n/2)(-1/2^ + (1/2)(-1/2)(-3/2)^ + %4 + • 1/(1 - x ) 2 = 1 +2x + 3x2 + 4x3 + 5x4 + , , , + u x ^ - 1 + , , , 7. Expand (1 +2x)7 8. Which is the coefficient of the term without an x in (x + 2/x) 1 1 . 9. 95) 11 . 10. Find the first 3 terms of the expansion of (1 + x) 1 / 4 .