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Composite function is a merge of multiple functions in simple form.
Typology: Lecture notes
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The Composition of Functions The composition of the function f with g is denoted by f g and is defined by the equation
The domain of the composite function f g is the set of all x such that
Example 3: Verify that each function is the inverse of the other. f (^) ( x) = 4 x + 9 and g (^) (x ) = x − 9 4 Finding the Inverse of a Function The equation for the inverse of a function can be found as follows:
b. f (^) (x ) = x 2
e. f (^) ( x) = 2 x + 1 Graphs of f and f − 1 The graphs of f and f − 1 are reflections of one another through the line y = x. Points on the graph of f − 1 can be found by reversing the coordinates of the points on the graph of f. Example 8: Consider the graph of the function f traced by joining the points given below with straight-line segments. Sketch the graph of f and the graph of f − 1 . Points on y = f(x) (^) Points on y = f − 1 (x) (−2,0) (0,1) (1,3)