assignment11 - University of Ottawa MAT 1320 - Assignment 1...

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University of Ottawa MAT 1320 - Assignment 1 Due: Tuesday, May 17 th , 2011 1. Find the domain of the following functions a) f ( x ) = x +1 ln ( x 2 - 1) b) g ( s ) = arccos ( | s - 1 | ) c) k ( z ) = z - 1 1 - z 2 2. Given f ( x ) = x + 1 x , g ( x ) = x +1 x +2 , find each of the following and their domains a) f g , g f and g g b) Evaluate f g (2) and g f (1) 3. Find the inverse of f ( x ) = 4 x - 1 2 x + 3 . You may assume that f ( x ) is a one-to-one function. 4. Solve the following a) exp(2 x + 3) = 7 b) 2 sin 2 ( x ) - sin( x ) - 1 = 0 c) | 2 - 3 x | < 7 5. Trigonometric functions a) Simplify sin(arcsin( x )) b) Sketch the graph of f ( x ) = - 2 cos(2 x ) + 1 and determine the ampli-
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