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7.7 Operations with Functions 7.8 Inverse of Functions

7.7 Operations with Functions 7.8 Inverse of Functions. Algebra II w/ trig. I. Operations on Functions A. Sum: B. Difference: C. Product: D. Quotient:. II. Find the sum, difference, product, and quotient: A. B. Composition of Functions. III. A. B.

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7.7 Operations with Functions 7.8 Inverse of Functions

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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

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