Pre-Calculus Practice Problem 107

Pre-Calculus Practice Problem 107 - 5. Which of the...

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Unit 3, Activity 6, Working with Exponential and Logarithmic Functions with Answers Blackline Masters, Advanced Math-Pre-Calculus Page 105 Comprehensive Curriculum, Revised 2008 2. Graph on the same set of axes: f(x) = 2 x and g(x) = log 2 x. What is the relationship of f(x) and g(x)? Each is the inverse of the other. If fx f x x x () () l o g == 2 1 2 then 3. Fill in the table below: f(g(x)) = f(x) g(x) Domain of f(g(x)) Domain of f Domain of g 1. ln(x 2 -4) Ln(x) x 2 -4 {x: x < -2 or x > 2} x > 0 Reals 2. e |x| e x | x | Reals Reals Reals 3. (1 – lnx) 2 x 2 1 – ln(x) x > 0 Reals x > 0 4. x 1 2 x 2 x 1 {x:x 0} Reals {x:x 0} 4. Which of the composite functions in the table above are even, odd, or neither? How do you know? 1 and 2 are even because they are symmetric over the y-axis. Numbers 3 and 4 are neither symmetric over the y-axis nor around the origin.
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Unformatted text preview: 5. Which of the functions in the table have an inverse that is a function? Justify your answer. Numbers 1, 2, and 3 do not have an inverse that is a function. Number 4 has an inverse that is a function. Justification: • Numbers 1, 2, and 3 are not-one-to-one functions or • because 1 and 2 are even functions they will not have an inverse that is a function, and number 3 decreases into a minimum then increases. • Looking at the graph or at the numerical tables of #4, the function is strictly decreasing, but y = 1 is a horizontal asymptote so the values of the range are never repeated. When x < 0, y < 1 and when x > 0, y > 1. 6. For those function/s that have an inverse find ) ( 1 x f − . The composite function in #4 has an inverse: ( ) 1 2 1 log ) ( − − = x x f...
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This note was uploaded on 10/10/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.

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