Stitz-Zeager_College_Algebra_e-book

6 1 3 3 3 4 x 4 x 3 3 0 x3 3x2 6x 8 x 1 r

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Unformatted text preview: y are switched. Similarly, the horizontal asymptote y = −2 of the graph of g corresponds to the vertical asymptote x = −2 of the graph of g −1 . 5.2 Inverse Functions 303 y 6 5 4 y=x 3 2 1 −6 −5 −4 −3 −2 −1 1 2 3 4 5 x 6 −1 −2 −3 −4 −5 −6 y = g (x) and y = g −1 (x) We now return to f (x) = x2 . We know that f is not one-to-one, and thus, is not invertible. However, if we restrict the domain of f , we can produce a new function g which is one-to-one. If we define g (x) = x2 , x ≥ 0, then we have y y 7 6 6 5 5 4 4 3 3 2 2 1 −2 −1 7 1 1 2 −2 −1 x restrict domain to x ≥ 0 y = f (x) = x2 −− − − − − − − − − − − − − −→ 1 2 x y = g (x) = x2 , x ≥ 0 The graph of g passes the Horizontal Line Test. To find an inverse of g , we proceed as usual y y x y y = = = = = g (x) x2 , x ≥ 0 y 2 , y ≥ 0 switch x and y √ ±x √ x since y ≥ 0 304 Further Topics in Functions √ We get g −1 (x) = x. At first it looks like we...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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