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1.5_The_Inverse_Function_Notebook

# 1.5_The_Inverse_Function_Notebook - (c Sketch a graph of...

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1.5__The_Inverse_Function.notebook 1 September 11, 2009 Inverse functions are a special class of functions that undo each other. The input and output for a pair of inverse functions f & g are shown : f(x) = 2x +1 and g(x)= (x-1)/2 Unit 1: Characteristics of Functions and Properties 1.5 Inverse Relations Recall D R D R 0 1 2 3 1 3 5 7 1 3 5 7 0 1 2 3 The inverse of a relation can be obtained by: Switching the x- and y-coordinates Switching the domain and range Reflecting the relation in the line y = x . The inverse of a function may or may not be a function. If the inverse is a function, then we denote it by f -1 (x). NOTE: (-1 is NOT an exponent) Recall f -1 (x) 1 f(x) (a) Find the inverse of each relation. (b) State the domain and range of the function and its inverse.

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Unformatted text preview: (c) Sketch a graph of the function and its inverse. (d) Determine if the inverse is a function. If it is not a f n , restrict the domain of the original f n to its principal branch , so that the inverse is a f n . Example 1 (i) y = x 2 +4x +5 (ii) y = √ x­1 (iii) x = y 2 + 1 1.5__The_Inverse_Function.notebook 2 September 11, 2009 Example 2 The area of a corn field (with a 400m perimeter)can be written as a function of its width using the following formula: A(w) = w ( 200 - w) a) Determine the inverse of this area function. b) What does the inverse represent? c) Find the width of the field if the area is 8700m 2 . Pair share...
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