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Understanding Operations and Inverses of Functions in Algebra II with Trigonometry

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cathleen-brown
10 diapositives · 233 Views · Nov 03, 2014

This resource covers the fundamental operations on functions, including sum, difference, product, and quotient. It demonstrates how to find these operations and illustrates composition of functions. Additionally, it delves into inverse functions and relations, detailing how to find an inverse by switching x and y values and verifying if two functions are inverses of each other. Students will learn through examples and have the opportunity to graph functions and their inverses. Essential for mastering Algebra II concepts with a trig focus.

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  1. 7.7 Operations with Functions7.8 Inverse of Functions Algebra II w/ trig

  2. I. Operations on Functions A. Sum: B. Difference: C. Product: D. Quotient:

  3. II. Find the sum, difference, product, and quotient: A.

  4. B.

  5. Composition of Functions III. A. B. Means: Plug g(x) into f(x) and simplify Means: Plug f(x) into g(x) and simplify

  6. C. Find f o g and g o f, if they exist 1. 2. 3.

  7. 7.8 Inverse Functions and Relations Relation: {(a,2), (b, 2), (c, 2)} This relation is a function because the x values are all different. To find the inverse of a relation switch the x and y values around. Inverse: {(2, a), (2, b), (2, c)}

  8. Property of Inverse Functions: Suppose f and f-1are inverse functions. Then, f(a) = b if and only if f-1(b) = a • Find the inverse function and graph the function and its inverse. • f(x) = x + 3 - rewrite f(x) as y - interchange x and y - solve for y - rewrite y as f-1

  9. f(x)= 2/3x – 1 • f(x) = 2x – 3 • f(x) = 2x + 1 3

  10. How to Verify Functions are Inverses: If f(g(x)) = x and g(f(x)) = x, then the functions are inverses of each other. • Determine whether each pair of functions are inverses functions. • f(x) = 3x – 1 g(x) = x + 1 3 2. f(x) = 2x + 5 g(x) = 5x + 2