Section 5.2 AN35 49. f g x f x x x x x x x x x x x x x g f x g x x x x x x x x x x x x x 4 3 2 2 4 3 2 3 4 3 2 4 2 4 3 3 2 4 3 4 2 5 5 , 2 2 3 4 4 2 3 4 3 2 2 3 4 4 2 3 3 4 2 4 2 3 5 5 , 4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − − = ⋅ − − + − − + = − + − − + − = = ≠ = + + = ⋅ + + − − + + = + − + + − + = = ≠ − 51. (a) f x x 1 3 1( ) = − f f x f x x x f f x f x x x 1 3 3 1 3 3 1 3 3 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) = = ⋅ = = = ⋅ = − − − (b) Domain of f f Range of All real numbers 1 = = − Range of f f Domain of All real numbers 1 = = − (c) y 5 x 5 y 5 x f(x) 5 3x f 21(x) 5 x 1 3 53. (a) f x x 4 1 2 1( ) = − − f f x f x x x x f f x f x x x x 4 1 2 4 4 1 2 2 2 2 4 2 4 2 4 1 2 1 2 1 2 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − = − + = − + = = + = + − = + − = − − − (b) Domain of f f Range of All real numbers 1 = = − Range of f f Domain of All real numbers 1 = = − (c) y 5 x 5 y 5 x f 21(x) 5 2 x 4 1 2 f(x) 5 4x 1 2 55. (a) f x x 1 1 3 ( ) = + − f f x f x x x f f x f x x x 1 1 1 1 1 1 1 3 3 3 1 1 3 3 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = + = + − = = − = − + = − − − (b) Domain of f f Range of All real numbers 1 = = − Range of f f Domain of All real numbers 1 = = − (c) y 5 x 5 y 5 x f(x) 5 x3 2 1 f 21(x) 5Ïx 1 1 3 57. (a) f x x x 4, 4 1( ) = − ≥ − f f x f x x x f f x f x x x x x 4 4 4 4 4 4 , 0 1 2 1 1 2 2 2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − = − + = = + = + − = = ≥ − − − (b) Domain of f f x x Range of 0 1 { } = = ≥ − Range of f f x x Domain of 4 1 { } = = ≥ − (c) y 8 x 8 y 5 x f(x) 5 x2 1 4, x $ 0 f 21(x) 5Ïx 2 4 59. (a) f x x 4 1 ( ) = − f f x f x x x f f x f x x x 4 4 4 4 4 4 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) = = = = = = − − − (b) Domain of f f x x Range of 0 1 { } = = ≠ − Range of f f x x Domain of 0 1 { } = = ≠ − (c) y 5 x 5 y 5 x f(x) 5 f 21(x) 5 4 x 61. (a) f x x x 2 1 1 ( ) = + − f f x f x x x x x x x x f f x f x x x x x 2 1 1 2 1 2 2 1 2 1 2 2 1 2 1 1 2 2 2 1 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) = + = + − = + − = = − = ⋅ − + − = + − = − − − (b) Domain of f f x x Range of 2 1 { } = = ≠ − Range of f f x x Domain of 0 1 { } = = ≠ − (c) y 5 x 5 y 5 x x 5 2 y 5 2 y 5 0 x 5 0 f 21(x) 5 2x 1 1 x f(x) 5 1 x 2 2 63. (a) f x x x 2 3 1 ( ) = − − f f x f x x x x x x x x x f f x f x x x x x x 2 3 2 3 2 3 2 3 2 3 2 2 2 3 2 3 2 3 2 3 2 3 3 2 2 2 2 1 1 1( ) ( ) ( ) ( ) ( ) ( ) ( ) = − = + − = + − = = = + = − ⋅ + + = + − ⋅ = = − − − (b) Domain of f f x x Range of 3 1 { } = = ≠ − − Range of f f x x Domain of 0 1 { } = = ≠ −
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