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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.
Multiplication Rule: Dependent Events The joint probability of two events A and B which are dependent is equal to the probability of A multiplied by the probability of B given
q5
Find the values of x and y
how to solve
Derivative with Polar Coordinates dy/dx = (dr/dθ (sin θ) + r cos θ) / (dr/dθ (cosθ) - r sinθ) Note: Rather than trying to keep in mind this formula it would possibly be easi
Seth has a pet goldfish. When he got his goldfish , it was only 5 centimeters long . Now it has grown to be 92 millimeters long. How many millimeters has the goldfish grown since
Maximize P=3x+2y Subject to x+y =6 x =3 x =0,y =0
how can i find the online students ?
If PA and PB are tangents to a circle from an outside point P, such that PA=10cm and ∠APB=60 o . Find the length of chord AB.
The first particular case of first order differential equations which we will seem is the linear first order differential equation. In this section, unlike many of the first order
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