7.6 – Function Operations

I. Operations with Functions All functions can be multiplied, divided, added, and subtracted All functions can be multiplied, divided, added, and subtracted *when dividing, remember to put in lowest terms via factoring if possible. *when dividing, remember to put in lowest terms via factoring if possible. Domain – any x – values the function covers Domain – any x – values the function covers

Example 1: compute the following if Example 1: compute the following if f(x) = x 2 -1 and g(x) = x + 1. –(f * g)(x) –f(x) / g(x) –(f + g)(x) –(f – g)(x)

II. Composition of Functions When two or more functions are combined, you form a composition of functions. When two or more functions are combined, you form a composition of functions. The output from the first function is used as an input into the next function. The output from the first function is used as an input into the next function. Work from the inside out, or back to front Work from the inside out, or back to front

For example: For example: f(x) = 2x + 3 f(x) = 2x + 3 g(x) = x g(x) = x g(f(3)) g(f(3)) First, compute f(3) = 2(3) + 3 = 9 First, compute f(3) = 2(3) + 3 = 9 Second, plug in 9 into g(x) = (9) = = 82 Second, plug in 9 into g(x) = (9) = = 82

Example 2: given the following functions, compute the following. Example 2: given the following functions, compute the following. f(x) = x – 2 g(x) = x 2 A)(f g)(x) B)(f g)(-5) C)(g f)(x) D)(g f)(11)

Example 3: The BMW dealer offers a 10% discount on a 7series. At the same time, the manufacturer offers a $2000 rebate for each purchaser. If the car cost $37, is it cheaper to apply the discount before or after the coupon? Example 3: The BMW dealer offers a 10% discount on a 7series. At the same time, the manufacturer offers a $2000 rebate for each purchaser. If the car cost $37, is it cheaper to apply the discount before or after the coupon?

Example 4: f(x) = 3x 2 + 2x – 8 and Example 4: f(x) = 3x 2 + 2x – 8 and g(x) = x + 2, and state domains g(x) = x + 2, and state domains : -f(x) + 4g(x) : f(x) * g(x) : 5f(x) / g(x)

Example 5: Let f(x) = 4x – 1. Find Example 5: Let f(x) = 4x – 1. Find [ f(x + h) – f(x) ] / h