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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.
Above we have seen that (2x 2 - x + 3) and (3x 3 + x 2 - 2x - 5) are the factors of 6x 5 - x 4 + 4x 3 - 5x 2 - x - 15. In this case we are able to find one facto
Surface Area with Polar Coordinates We will be searching for at surface area in polar coordinates in this part. Note though that all we're going to do is illustrate the formu
What is Congruent Number?
Tests for relative minimum For a relative minimum point there are two tests: i.The first derivative, which is (dy)/(dx) = f´(x) = 0 ii.The second derivative, which i
what is the first step
6 412.56356
smart mind
v=u+at s=ut+1/2at^2
How do I choose a distribution test for a sample size of 60? Probability of rolling a 4 on a six sided die.
Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.
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