(a) Find f-1(x)
The function g has domain –1 ≤ x ≤ 8, and is linear from (–1, –9) to (2, 0) and from
(2, 0) to (8, 4). Figure 2 shows a sketch of the graph of y = g(x).
(b) Write down the range of g.
(c) Find gg(2).
(d) Find fg(8).
(e) On separate diagrams, sketch the graph with equation
(i) y = |g(x)| ,
(ii) y = g-1(x)
Show on each sketch the coordinates of each point at which the graph meets or cuts the axes.
(f) State the domain of the inverse function g-1.
(a) Show that
dy/dx = (6 sin 2x + 4 sin 2x + 2)/(2 + cos 2x)2
(b) Find an equation of the tangent to C at the point on C where x = π/2
Write your answer in the form y = ax + b, where a and b are exact constants.7(a)
(c) Hence find dy/dx in terms of x.8 (a)
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