6.3 “Function Operations & Composition”

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Presentation transcript:

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

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

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

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

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

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

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

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.

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.