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Unformatted text preview: – A: x3(x2 – 2) B: (x2 – 2)3 – C: (x3)2 – 2 C: (x2 – 2)3(x) Example • From tables – f(g(2))= – A: 2 B: 1 – C: 0 D: 3 – g(g(1)) = – A: 2 B: 1 – C: 4 D: 0 x f(x) g(x) 2 3 1 1 2 2 1 3 3 Example • From graphs – f(g(2))= – A: 3 B: 2 C: 4 D: does not exist – g(g(1)) = – A: 1 B: 5 C: 4 D: does not exist Examples • f(x) = 2x – 3 and g(x) = (x+3)/2 – f(g(x)) = – g(f(x)) = • f(x) = x2 and g(x) = sqrt (x) – f(g(x)) = – g(f(x)) = • f(x) = 10x and g(x) = log10x – f(g(x)) = – g(f(x)) = Inverse Functions • These last three were examples of inverse functions • Whenever f(g(x))=x AND g(f(x))=x for all x • The functions are inverses of each other. • We write g(x) = f1(x) and f(x) = g1(x) • Here the inverse is the functional inverse (not the multiplicative inverse) Assignment 8.8 • 8.8: p. 533: Algebra Aerobics: 13 • p. 543: Algebra Aerobics: 13 • p. 543544: Exercises: 1, 3 • Due May 9, 2011...
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 Spring '11
 Continuous function, Inverse function, Master subtitle style

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