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Unformatted text preview: Sec2728Notes.notebook October 05, 2009 Section 2.7 Combining Functions Let ‘f’ and ‘g’ be functions with domains A and B. Then we can define the following functions: Use as example functions. Composition of two functions 1 Sec2728Notes.notebook October 05, 2009 Find the original functions given the end result: 2 Sec2728Notes.notebook October 05, 2009 (2.7 #33) Find the following functions and give their domains. Sec. 2.8 Inverse Functions
A function ‘f’ with domain A is called a “onetoone function” if no two values of ‘x’ have the same image (value of f(x)).
or, if then No Horizontal line intersects the graph more than one time 3 Sec2728Notes.notebook October 05, 2009 Deciding if a function is OnetoOne
Which of the following are “onetoone”? Is h(t) a onetoone function? 4 Sec2728Notes.notebook October 05, 2009 Inverse of a ‘onetoone’ function
Let be a onetoone function with Domain A and Range B. Then we can define its ‘inverse function’ with Domain B and Range A by An inverse function “undoes” the rule that a function “does”.
If a function multiplies by 2, the inverse divides by 2.
If a function takes ‘radius’ and gives ‘area’, the inverse takes ‘area’ and gives the corresponding ‘radius’.
If a function takes degrees Fahrenheit and gives degrees Celsius, then the inverse takes Celsius and gives Fahrenheit. Showing two functions are inverses of each other Finding the inverse of a onetoone function
Write Solve the equation for ‘y’ in terms of ‘x’ (if possible)
Interchange ‘x’ and ‘y’ to get 5 Sec2728Notes.notebook October 05, 2009 Find the inverse function for f(x) Show that the two functions are inverses of each other.
Compare their graphs... 6 Sec2728Notes.notebook October 05, 2009 Find the inverse function of f(x) Sketch the graph. Then sketch its inverse. Then find the equation for the inverse function. 7 ...
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- Fall '06