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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.
Linear functions are of the form: y = a 0 + a 1 x 1 + a 2 x 2 + ..... + a n x n where a 0 , a 1 , a 2 ..... a n are constants and x 1 , x 2 ..... x n a
A boy covered half of distance at 20km/hr and rest at 40kmlhr. calculate his average speed.
#Mai iss 3 years younger than twice the age of her brother . If b represents the age of Mai''s brother .which expression below represents Mai''s age 2-3b 3-2b 2b-3 3b-2 2-3b 3-2b q
sin((2n+1)180)
Q. How many permutations can you make of the word STATISTICS? Solution: There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'
Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
I am greater than 30 and less than 40. The sum of my digits is less than 5. who am I?
The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.
what is the volume of new ipad pro box
Ask question #Minimum 100 words acca paper mill produces two grades of paper viz.,xand y.Bacause of raw material restrictions, it cannot produce more than 400 tones of grade x pape
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