7.7 Operations with Functions 7.8 Inverse of Functions Algebra II w/ trig.

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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.

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

C. Find f o g and g o f, if they exist

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)}

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

B.f(x)= 2 / 3 x – 1 C.f(x) = 2x – 3 D.f(x) = 2x + 1 3

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