Stitz-Zeager_College_Algebra_e-book

# G x 2 4 x3 3 hx 3 4 k x 8x x1 2x x2

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Unformatted text preview: from g and returns them to their respective inputs. We now have enough background to state the central deﬁnition of the section. Definition 5.2. Suppose f and g are two functions such that 1. (g ◦ f )(x) = x for all x in the domain of f and 2. (f ◦ g )(x) = x for all x in the domain of g . Then f and g are said to be inverses of each other. The functions f and g are said to be invertible. Our ﬁrst result of the section formalizes the concepts that inverse functions exchange inputs and outputs and is a consequence of Deﬁnition 5.2 and the Fundamental Graphing Principle for Functions. Theorem 5.2. Properties of Inverse Functions: Suppose f and g are inverse functions. • The rangea of f is the domain of g and the domain of f is the range of g • f (a) = b if and only if g (b) = a • (a, b) is on the graph of f if and only if (b, a) is on the graph of g a Recall this is the set of all outputs of a function. The third property in Theorem 5.2 tells us that the graphs of inverse functions are reﬂections about the line y = x. Fo...
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