Pre-Calculus Practice Problem 107

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

This preview shows page 1. Sign up to view the full content.

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.
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online