MAT135H1 Lecture Notes - Lecture 3: Function Composition, Inverse Function
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MAT135H1 Full Course Notes
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Mat135 - lecture 3 - composite and inverse functions. New functions from old functions (cont"d from lecture 2: remember: domain of (f + g) = domain of (f - g) = domain of (f g) = domain of f and domain of g (i. e. overlapping area) Composite functions: given two functions f and g, the composite function f (cid:0) g is given by (f (cid:0) g)(x) = f(g(x)) Domain of composite functions: in order for (f (cid:0) g)(x) to make sense, g(x) must make sense, and then f must make sense at g(x) I. e. we need x to be an element of the domain of g, and g(x) must be an element of the domain of f. Namely, f(x1) f(x2) if x1 x2. Any one-to-one function f has an inverse function f-1. Further, f-1 is defined by f-1(g) = x (cid:0) f(x) =y.
