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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.
The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles. Find the length of the boundary and the area of the shaded portion
Example of Fractional Equations: Example: Solve the fractional equation (3x +8)/x +5 =0 Solution: Multiply both sides of the equation by the LCD (x). (x) ((3x
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the sides of a right angle triangle are a,a+d,a+2d with a and d both positive.the ratio of a to d a)1:2 b)1:3 c)3:1 d)5:2 answer is (c) i.e. 3:1 Solution: Applying
Mike, Dan, Ed, and Sy played together on a baseball team. Mike's batting average was 0.349, Dan's was 0.2, Ed's was 0.35, and Sy's was 0.299. Who had the highest batting average?
The Laplace method Laplace method employs all the information by assigning equal probabilities to the possible payoffs for every action and then selecting such alternative whic
joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the
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