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ARC 1999S - SUGGESTED SOLUTIONS for 3 UNIT MATHS 1999...

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SUGGESTED SOLUTIONS for 3 UNIT MATHS - 1999 Question One (a) 1 ) ( + = = x e y x f 1 + = y e x x y ln 1 = + 1 ln = x y the inverse function ) ( 1 x f )] ( [ 1 x f f 1 1 ln + = x e x e x = = ln x x e x e x f f x = + = + = = + 1 1 1 ln ) 1 ( 1 ] ln[ )] ( [ 1 1 (b) 3 2 2 1 + x x 2 2 ) 2 )( 3 ( 2 ) 2 ( ) 3 ( + + x x x x 0 ) 2 )( 3 ( 2 ) 2 ( ) 3 ( 2 2 + + x x x x 0 )] 2 ( 2 3 )[ 2 )( 3 ( + + x x x x 0 ] 4 2 3 )[ 2 )( 3 ( + x x x x 0 ) 7 )( 2 )( 3 ( + x x x ……….(1) Consider 0 ) 7 )( 2 )( 3 ( = + x x x Test x = -10, inequality (1) holds true Test x = -5, inequality (1) does not hold true Test x = 0, inequality (1) holds true Test x = 4, inequality (1) does not hold true Solution is 7 x or 3 2 < < x ) 3 ( ), 2 ( x x From the graph of ) 7 )( 2 )( 3 ( + = x x x y -7 -2 3 0 y x -7 -2 3
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