100922 More problems on inverses

For calculating inverses exchange x s and y s then

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for calculating inverses (exchange x ’s and y ’s, then solve for y ). a. Given f ( x ) = –2 x + 3, calculate an equation for the inverse function f –1 ( x ). Next, graph f ( x ) and f –1 ( x ) on the same grid. Finally, visually confirm that the two graphs are reflections of each other, and add the “mirror line” to your picture. b. Calculate the inverse for the general linear function f ( x ) = mx + b . How are the slopes of the original line and the inverse line related? c. Are there any lines f ( x ) = mx + b for which the inverse is not a function? Explain why. 4. A graph of v ( x ) is given on the grid below. a. Is v ( x ) a one-to-one function? Justify your answer. b. On graph paper in a single graphing plane, draw graphs of v ( x ) and its inverse. Explain why the inverse isn’t a function. c. Find a restriction of the domain of v ( x ) so that the restricted graph will be one-to-one. d. Using your restriction from part c , graph the restricted v ( x ) and its inverse function v –1 ( x ). e. Find a second possible answer to part c .

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Name Honors Algebra 2 Problem set page 2 5. Here are two functions that you’ve seen on a previous assignment: E = f ( S ) and C = g ( E ). a. Is the inverse of f also a function? If yes, make a table of values and a graph for the inverse function f –1 . If no, explain why not.
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