Section7_1_review

Section7_1_review - f o f-1 = f f-1 (29 = x f-1 o f = f-1 f...

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Section 7.1: Inverse Functions The inverse of a one-to-one function f x ( 29 is f - 1 x (29 , where a one-to-one function is a function which never takes on the same value twice and therefore passes the Horizontal Line Test. The domain of f - 1 x (29 is the range of f x ( 29 , and the range of f - 1 x (29 is the domain of f x ( 29 . The graph of f - 1 x (29 is obtained by reflecting the graph of f x ( 29 about the line y = x . Therefore, if a , b ( 29 is an ordered pair on the graph of f x ( 29 , then b , a ( 29 is on the graph of f - 1 x (29 . In other words, if f a (29 = b , then f - 1 b (29 = a . To determine the inverse of a one-to-one function f x ( 29 : (i) Write the function as y = f x (29 . (ii) Solve for x in terms of y , if possible. (iii) Interchange x and y . (This is done to express the inverse function as a function of x , which is traditionally the independent variable.) (iv) Express as y = f - 1 x (29 . (v) Optional check – Use the cancellation equations:
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Unformatted text preview: f o f-1 = f f-1 (29 = x f-1 o f = f-1 f (29 = x Problem. Find the inverse function of fx (29 = x-5 . Solution. y = x-5 y 2 = x-5 x = y 2 + 5 y = x 2 + 5 f-1 x (29 = x 2 + 5 Problem. Find the inverse function of f x ( 29 = x-2 x + 5 . Solution. y = x-2 x + 5 x + 5 ( 29 y = x-2 xy + 5 y = x-2 xy-x =-5 y-2 y-1 ( 29 x =-5 y-2 x =-5 y-2 y-1 y =-5 x-2 x-1 f-1 x (29 =-5 x-2 x-1 Problem. Find the domain and range of the inverse function for fx (29 = 3 + 7 x . Solution. Domain of the function is 3 + 7 x , or x -3 7 , so -3 7 , . Range of the function is 0, [ 29 . Therefore, domain of the inverse function is 0, [ 29 . Range of the inverse function is -3 7 , ....
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This note was uploaded on 01/12/2010 for the course MATH 44245 taught by Professor Famiglietti during the Fall '07 term at UC Irvine.

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Section7_1_review - f o f-1 = f f-1 (29 = x f-1 o f = f-1 f...

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