Math1011_Week04_Prelim1A - Math1011 - Learning Strategies...

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Math1011 - Learning Strategies Center Section 1.6 IA-1 The function f(x) is graphed below: -4 -3 -2 -1 0 1 2 3 4 0 1 2 3 4 What is the domain and range of the f(x)? Is f(x) one-to-one? Why? Sketch f -1 (x) in the graph above. What is the domain and range of f -1 (x)?
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Math1011 - Learning Strategies Center Section 1.6 A1 The function f(x) is graphed below: -4 -3 -2 -1 0 1 2 3 4 - 4 - 3 - 2 - 101234 What is the domain and range of the f(x)? The domain of is ( 1, ) The range of is ( ,1) f −∞ −∞ Is f(x) one-to-one? Why? The function is one-to-one as its graph intersects each horizontal line at most once (Horizontal Line Test). Sketch f -1 (x) in the graph above. What is the domain and range of f -1 (x)? 1 1 The domain of is ( ,1). The range of is ( 1, ). −∞ (Doc #011w.16.06t)
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Math1011 - Learning Strategies Center Section 1.6 A2 -1 -1 Show that the function f is one-to-one, and calculate the inverse function f . Specify the domain and range of f and f . 1 () x fx + =
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Math1011 - Learning Strategies Center Section 1.6 A2 -1 -1 Show that the function f is one-to-one, and calculate the inverse function f . Specify the domain and range of f and f . 1 () x fx + = 12 1 2 11 21 1 2 1 To show one-to-one, show if f(x ) ( ) x f(x ) ( ) (cross multiply) x (1 ) x (1 ) (distribute) x x x x (subtract x from both sides) x i s o xx ++ + = ⇒= = = += + + = = 1 2 -1 1 1 1 ne-to-one as f(x ) ( ) x Calculate the inverse function f ( ). (solve for x in terms of y) (1 ) (cross multiply) ) y yx + =⇒ = = =− = = -1 1 1 interchange x and y Specify the domains and ranges of f and f . ( ) ( ,1 ) (1 , ) ( ) ( , 1 ) ( 1 Df f fD =ℜ = −∞− ∪ − ∞ ℜ= = (Doc #011w.16.07t)(Adams 3.1.10)
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Math1011 Fall 2007 Prelim A3 Show that for any three positive numbers a, b, c such that a 1, b 1, and c 1, the following equality holds: (log )(log )(log ) 1 ac b bca = Solve the equation for x: 4 2log 1 10 ln 4 log 100 x e +=
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Math1011 Fall 2007 Prelim A3 Show that for any three positive numbers a, b, c such that a 1, b 1, and c 1, the following equality holds: (log )(log )(log ) 1 ac b bca = log log log log (log )(log )(log ) 1 (log )( )( ) 1 (log aa ca a bc = = log )( c log log log )( )1 log 1 1 1
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This note was uploaded on 11/22/2009 for the course CHEM 2070 at Cornell University (Engineering School).

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Math1011_Week04_Prelim1A - Math1011 - Learning Strategies...

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