AN36 Answers: Chapter 5 65. (a) f x x x 2 3 1( ) = − − − f f x f x x x x x x x x x x x f f x f x x x x x x x x x x x 2 3 3 2 3 2 3 2 3 2 2 2 3 6 6 3 2 2 3 2 3 2 3 2 3 3 3 2 6 6 1 1 1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − − = ⋅ − − − − + = − − + − = − − = = + = − ⋅ + + − = − ⋅ − + = − − = − − − (b) Domain of f f x x f f x x Range of 2 ; Range of Domain of 3 1 1 { } { } = = ≠ − = = ≠ − − 67. (a) f x x x3 2 1( ) = − − f f x f x x x x x x x x x x x f f x f x x x x x x x x x x x 3 2 2 3 2 3 3 2 1 2 3 3 2 2 2 2 3 1 2 3 1 3 2 3 1 2 2 6 2 3 1 2 2 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − = ⋅ − ⋅ − − = − − = = = − = − ⋅ − − = − − = = − − − (b) Domain of f f x x f f x x Range of 1 3 ; Range of Domain of 2 3 1 1 { } { } = = ≠ = = ≠ − − 69. (a) f x x x 3 4 2 3 1( ) = + − − ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = + − = ⋅ + − + ⋅ + − − = + + − + − − = = = + − = ⋅ + − + ⋅ + − − = + + − + − − = = − − − f f x f x x x x x x x x x x x x f f x f x x x x x x x x x x x x 3 4 2 3 3 3 4 2 3 4 2 3 4 2 3 3 3 3 4 4 2 3 2 3 4 3 2 3 17 17 3 4 2 3 3 3 4 2 3 4 2 3 4 2 3 3 3 3 4 4 2 3 2 3 4 3 2 3 17 17 1 1 1 (b) Domain of f f x x f f x x Range of 3 2 ; Range of Domain of 3 2 1 1 { } { } = = ≠ = = ≠ − − 71. (a) f x x x 2 3 2 1( ) = − + − − ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − + − = ⋅ − + − + − + − + = − + + − − + + − = − − = = + + = − ⋅ + + + + + − = − + + + + − + = − − = − − − f f x f x x x x x x x x x x x x f f x f x x x x x x x x x x x x 2 3 2 2 2 3 2 3 2 3 2 2 2 2 3 3 2 2 3 2 2 1 2 3 2 2 2 3 2 3 2 3 2 2 2 2 3 3 2 2 3 2 2 1 1 1 1 (b) Domain of f f x x f f x x Range of 2 ; Range of Domain of 2 1 1 { } { } = = ≠ − = = ≠ − − 73. (a) f x x 2 1 2 1( ) = − − f f x f x x x x x x f f x f x x x x x x x x 2 1 2 4 1 2 4 2 4 1 2 4 4 1 2 2 4 8 8 4 2 2 1 2 4 2 2 4 , since 0 1 1 1 2 2 2 2 2 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − = − − ⋅ − = − − ⋅ = = = − = − ⋅ − = = = > − − − (b) Domain of f f x x f f x x Range of 0 ; Range of Domain of 1 2 1 1 { } { } = = > = = < − − 75. (a) f x x x 4 , 4 1 3 2 ( ) ( ) = + ≥− − f f x f x x x x f f x f x x x x x 4 4 4 4 4 4 4 4 , since 0 1 1 1 3 2 3 2 2 3 2 3 2 3 3 2 2 3 3 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = + = + − = + − = = − = − + = = ≥ − − − (b) Domain of f f x x Range of 0 ; 1 { } = = ≥ − Domain of f f x x Range of 4 1 { } = = ≥− −
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