Stitz-Zeager_College_Algebra_e-book

2 3 we now create our sign diagram and nd 32 x13 x2

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s natural to wonder what f −1 (x) and g −1 (x) would be. For f (x) = 1−2x , we can 5 think our way through the inverse since there is only one occurrence of x. We can track step-by-step what is done to x and reverse those steps as we did at the beginning of the chapter. The function g (x) = 12xx is a bit trickier since x occurs in two places. When one evaluates g (x) for a specific − value of x, which is first, the 2x or the 1 − x? We can imagine functions more complicated than these so we need to develop a general methodology to attack this problem. Theorem 5.2 tells us equation y = f −1 (x) is equivalent to f (y ) = x and this is the basis of our algorithm. Steps for finding the Inverse of a One-to-one Function 1. Write y = f (x) 2. Interchange x and y 3. Solve x = f (y ) for y to obtain y = f −1 (x) Note that we could have simply written ‘Solve x = f (y ) for y ’ and be done with it. The act of interchanging the x and y is there to remind us that we are finding the inverse fun...
View Full Document

Ask a homework question - tutors are online