1007Test1_09

1007Test1_09 - in degrees is………… c The range of the...

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Test 1, Wednesday January 28, 2009 MATH 1007G Last Name :_________________ First Name:_______________ ID #:____________________ Total marks:36 Total time: 50 minutes No Calculators are allowed. Show your work. Question 1. [3 marks] Find an expression for the function f whose graph is the straight line through the points ( , ) 3 5 and ( , ) 2 4 - in the xy - plane. Question 2. a) [3 marks] Find all the values of x in [ ] 0 2 , π such that 2 2 0 sin sin cos x x x + = . Question 3. [10 marks] Simplify a) log log log 2 2 2 15 6 20 - - b) log (ln ) ( )ln 5 5 1/2 2 e e x x - c) 3 12 4 3 2 x y x x y + where x < 0 while y 0 . d) ( ) / 27 6 4 3 x - e) cos(tan ) - 1 x Question 4. [2 marks] Find ( )( ) f f x r when f x x ( ) = - 2 1 . Simplify the result as much as possible. Question 5. [3 marks] Fill in the blank. a) Find cos 2 3 =…………………… b) Does α = 5 12 radian, then the measure of the angle
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Unformatted text preview: in degrees is…………. . c) The range of the tan-1 function is ………………. Test 1, Wednesday January 28, 2009 MATH 1007G Question 6. [3.5 marks] Remove the absolute value in f x x x ( ) = + -1 2 2 (i.e. write f as a function defined “piecewise”) Question 7. Let f x x ( ) =-1 5 a) [3 marks] Find the domain and range of the function. b) [3 marks] Find a formula for the inverse function f-1 (if possible) or explain why f-1 does not exist. Question 8. [2.5 marks] If tan θ = 1 2 and - < < -π / 2 , find sin . Question 9. [3 marks] A graph of f is given. Sketch the graph of a) the inverse function f-1 b) the function g x f x ( ) ( ) = -...
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1007Test1_09 - in degrees is………… c The range of the...

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