(d) Find the domain and the range of f (x) = x2 16 5 . [9]

2. Consider the quadratic function f (x) = 3 + 2x x2 . (a) Express f (x) in standard form. (b) Find the coordinates of the vertex and indicate whether it corresponds to the maximum or the minimum of f . (c) Find the x and y intercepts. (d) Sketch the graph of f (x) using the information above. [9]

3. (a) Let f (x) = 53x 4 2. Find the inverse function f 1 (x). (b) Let f (x) = ex+1 and g (x) = ln(x 1). Find g f and determine its domain. [12] 4. Find the solutions of the following equations: (a) 22x 2x+3 20 = 0 (b) log3 x + log3 (x + 2) 2 = 0 MATH 201 [12] 5. Final Examination December 2012 Page 2 of 2 Find the solutions of the following equations: (a) 2 2x 8x = 0 (b) log5 (x + 1) log5 (x 1) = 2 [9] 6. (a) Find the radius of the circle if its sector with a central angle 1 = radian has an area A = 9 m2 . 2 (b) A car s wheels are 70 cm in diameter. What is the speed of the car in km/hour if the wheels rotate at 180 revolutions per minute ? [12] 7. Solve the triangle ABC (i.e. nd the missing sides and angles) (a) A = 30 B = 70 b = 30 cm (b) A = 53 b = 15 cm c = 20 cm [9]

8. 1 (a) Find the amplitude period and phase shift of y = 3 sin[ (x 3 )]

(b) A ladder leans against a vertical wall of a building so that the angle between the ground and the ladder is 72 and its bottom on the ground is at 3 m from the wall. How long is the ladder? How high does it reach? [6]

9. Verify the identities sin x 1 cos x =0 sin x 1 + cos x cot x (b) csc x sin x = sec x (a) [10] 10. Solve the following trigonometric equations in [0 2 ] (a) (b) [5] 11. sin2 x + sin x = cos2 x sin 2x cos x + cos 2x sin x = 1 Bonus Question If a function f (x) is dened for all real x and has an inverse f 1 (x) does it necessarily follow that also g (x) = [f (x)]2 has an inverse g 1 (x) ? Explain why it does or give an example when it does not.

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