G x 2 4 x3 3 hx 3 4 k x 8x x1 2x 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: 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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online