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inequalities assignment 3 - Assignment 3 Inequalities Due...

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Assignment 3: Inequalities Due: 8 th October Name: _______________________ 1. Find the values of x for which 5 – 3 x x + 1 . Working: Answer: .......................................................................... (Total 3 marks) 2. Solve the inequality x 2 – 4 + x 3 < 0. Working: Answer: .......................................................................... .......................................................................... (Total 6 marks) 1
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3. Solve the inequality x – 2 2 x + 1 . Working: Answer : ......................................................................... (Total 6 marks) 4. Let f ( x ) = 1 4 + + x x , x –1 and g ( x ) = 4 2 x x , x 4. Find the set of values of x such that f ( x ) g ( x ). Working: Answer : ......................................................................... (Total 6 marks) 2
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5. Solve the inequality 9 9 - + x x 2 Working: Answer : ......................................................................... (Total 6 marks) 6. Let f ( x ) = 1 4 + + x x , x ≠ –1 and g ( x ) = 4 2 - - x x , x ≠ 4. Find the set of values of x such that f ( x ) g ( x ). ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... (Total 6 marks) 3
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6. Let f ( x ) = 2 5 5 2 + + + x x x , x –2. (a) Find f ( x ). (b) Solve f ( x ) > 2. W o r k i n g : A n s w e r s : ( a ) ( b ) (Total 6 marks) 7. The functions f and g are defined by f ( x ) = 2 x −1, g ( x ) = . x , x x 1 1 - + Find the values of x for which ( f g ) ( x ) ≤ ( g f
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