6.3 “Function Operations & Composition”

Operations on FunctionsOperation Definition Example: f(x) = 5x, g(x) = x + 2 Add h(x)= f(x) + g(x) h(x) = 5x + (x + 2) = 6x + 2Subtract h(x)= f(x) - g(x) h(x) = 5x – (x + 2) = 4x – 2 Multiply h(x)= f(x) · g(x) h(x) = 5x(x+2) = 5x2 + 10xDivide h(x) = h(x) =

Add & Subtract Functions1. Let f(x) = 4x½ and g(x) = -9x½

a. Find f(x) + g(x)

b. Find f(x) - g(x)

Multiply & Divide Functions2. Let f(x) = 6x and g(x) = x¾

a. Find f(x) · g(x)

b. Find

Find Compositions of Functions3. Let f(x) = 4x-1 and g(x) = 5x – 2

a. Find f(g(x))

b. Find f(f(x))

c. Find g(f(x))

d. Find the domain of each

Practice – Add & Subtract1. Let f(x) = -2x⅔ and g(x) = 7x⅔

a. Find f(x) + g(x)

b. Find f(x) - g(x)

Practice – Multiply & Divide2. Let f(x) = 3x and g(x) = x⅕

a. Find f(x) · g(x)

b. Find

Practice - Compositions3. Let f(x) = 2x2 and g(x) = 3x – 8

a. Find f(g(x))

b. Find f(f(x))

c. Find g(f(x))

d. Find the domain of each

Word ProblemsFor a white rhino, heart rate r (in beats per minute) and life span s (in minutes) are related to body mass m (kilograms) by these functions:r(m) = 241m-0.25

s(m) = (6 x 106)m0.2

a. Find r(m) · s(m)

b. Explain what this product represents.

Practice - Word ProblemsUse the result in the last example to find a white rhino’s number of heartbeats over its lifetime if its body mass is 1.7 x 105 kilograms.