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# Functions 2 inverse , composite

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### Functions 2 inverse , composite

1. 1. 1Ago 28­06:11 p.m.Composition of functionsInverse functionBy the end of the lesson you will be able to:• Understand and use composite functions.• Understand and use  inverse  functions.http://www.youtube.com/watch?v=GW3Sq6Ez9zA
2. 2. 2Ago 28­06:11 p.m.Starter:With your calculator draw the graph of  y= ex.State domain, range and asymptotes of this function.
3. 3. 3Ago 28­06:11 p.m.Composition of functionsIf   andfind in simplest form:
4. 4. 4Ago 28­06:11 p.m.Given the functions andfind
5. 5. 5Ago 28­06:11 p.m.xf(x)f gg(f(x))For  to exist, then  range of f must be  included in the domain of g.
6. 6. 6Ago 28­06:11 p.m.Indentity function:What happens when this function is composed with anotherfunction?g(x) = 2 x ­ 3==
7. 7. 7Ago 28­06:11 p.m.Inverse functionx f(x)ff ­1The inverse of a function exists if and only if the function is aone-to-one function.
8. 8. 8Ago 28­06:11 p.m.Which of these functions have an inverse?
9. 9. 9Ago 28­06:11 p.m.Find the inverse of :draw the graphs of both functions. Draw theidentity function on the same graph.and
10. 10. 10Abr 30­05:32 p.m.y = 3x+2y = x
11. 11. 11Ago 28­06:11 p.m.The graph of is a reflection of the graph ofabout the line y = xFind the inverse function ofand sketch both graphs.
12. 12. 12Sep 12­02:30 p.m.
13. 13. 13Ago 28­06:11 p.m.Find the inverse function of Draw the graphs of both functions.is a self­inverse function
14. 14. 14Ago 28­06:11 p.m.Find the inverse function offor x≠1 and sketch both graphs.