MAT_1143-may_6 - – A x3(x2 – 2 B(x2 – 2)3 – C(x3)2...

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Click to edit Master subtitle style May 6, 2011 Sections 8.8
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Exam 4 We are on schedule for Exam 4 to be Wednesday, May 11. It will cover Section 7.1-8.8 (the parts we cover) Last new material today
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Final Exam Friday, May 13 and Monday, May 16 we review for the final exam We have actually been reviewing some daily as we get new functions and compare them to old functions. Final is Wednesday, May 18, 10:30-12:30 (for 11 am section) or 1-3 pm (for 2 pm section) Probably schedule a review session on Tuesday, May 17 before the final.
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One More New Function from Old Composition (f l g)(x) = f(g(x)) We apply g to the input x. This entire expression becomes the input to the function f. This is NOT (f*g)(x) = f(x)*g(x)— multiplication, which we did last lecture.
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Example f(x) = x3 and g(x) = x2 – 2 f(g(2))= A: 0 B: 8 C: 16 D: does not exist g(g(1)) = A: 1 B: -1 C: -3 D: does not exist
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Example f(x) = x3 and g(x) = x2 – 2 f(g(x)) = A: x3(x2 – 2) B: (x2 – 2)3 C: (x3)2 – 2 C: (x2 – 2)3(x) g(f(x)) =
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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) = f-1(x) and f(x) = g-1(x) • Here the inverse is the functional inverse (not the multiplicative inverse) Assignment 8.8 • 8.8: p. 533: Algebra Aerobics: 1-3 • p. 543: Algebra Aerobics: 1-3 • p. 543-544: Exercises: 1, 3 • Due May 9, 2011...
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