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lesson 8 and 9
unit 1 ms brown
| Term | Definition |
|---|---|
| Composition of Functions | a function made of other functions, where the output of one function is the input of another function (f×g)(x)=f(g(x)): "f of g", indicates that g(x) is the input to f(x). |
| Not commutative | the property that order DOES matter when composing |
| Restricted domain | a domain for a function that is smaller than the function's domain of definition; typically used to specify a one-to-one section of a function |
| Decomposition | breaking a given composed equation into the inner and outer function |
| --------------------------------------------------------------------------------- | --------------------------------------------------------------------------------- Lesson 9 |
| Inverse relation | a set of ordered pairs obtained by interchanging the first and second coordinates of each pair in the original function |
| Horizontal Line Test | a test consisting of drawing horizontal lines through a function to prove whether it is one-to-one and therefore has an inverse that is also a function. |
| One-to-One | any output value, y, in a function has exactly one input, x. If a function is one-to-one, then it has an inverse that is also a function. |
| inverse Function | a function that undoes the action of another function. A function g is the inverse of a function f if y=f(x) then x=g(y) |
| f-1(x)= | F inverse |
| Inverse reflection Principle | a function and its inverse will be reflections of each other over the line y=x |
| Inverse Composition Rule | when f and g are inverse, the composition of f and g (in either order) creates a function that for every input returns the input: f(g(x))=g(f(x))=x |
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