1. 6.3 “Function Operations & Composition”
Operations on Functions
Operation Definition Example: f(x) = 5x, g(x) = x + 2
Add h(x)= f(x) + g(x) h(x) = 5x + (x + 2) = 6x + 2
Subtract 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 + 10x
Divide h(x) = 𝑓(x) 𝑔(x) h(x) = 𝟓𝐱 𝐱+𝟐

2. Add & Subtract Functions
Let f(x) = 4x½ and
g(x) = -9x½
a. Find f(x) + g(x)
b. Find f(x) - g(x)

3. Multiply & Divide Functions
Let f(x) = 6x and
g(x) = x¾
a. Find f(x) · g(x)
Find 𝐟(𝐱) 𝐠(𝐱)

4. Find Compositions of Functions
Let f(x) = 4x-1 and
g(x) = 5x – 2
a. Find f(g(x))
b. Find f(f(x))
Find g(f(x))
Find the domain of each

5. Practice – Add & Subtract
Let f(x) = -2x⅔ and
g(x) = 7x⅔
a. Find f(x) + g(x)
b. Find f(x) - g(x)

6. Practice – Multiply & Divide
Let f(x) = 3x and
g(x) = x⅕
a. Find f(x) · g(x)
Find 𝐟(𝐱) 𝐠(𝐱)

7. Practice - Compositions
Let f(x) = 2x2 and
g(x) = 3x – 8
a. Find f(g(x))
b. Find f(f(x))
Find g(f(x))
Find the domain of each

8. Word Problems
For 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.

9. Practice - Word Problems
Use 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.