Decomposing Functions

Composite Functions Lessons

Elizabeth Borres

At the end of the lesson, students will be able to:

• Define composite functions.

• Solve composite functions.

• Apply composite functions in real life.

Let us have a short review.

(Function Operations)

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(f+g\right)\left(0\right)=$$

• $$-1$$  

• $$3$$  

• $$1$$  

• $$-3$$  

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(f-g\right)\left(1\right)=$$

• 3

• -3

• 1

• -1

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(f\cdot g\right)\left(-1\right)=$$

• -3

• -14

• 14

• -7

Multiple Choice

If $$f\left(x\right)\ =\ x-1$$ and $$g\left(x\right)=5x-2$$ , then  $$\left(\frac{f}{g}\right)\left(\frac{2}{5}\right)$$

• undefined

• $$\frac{1}{3}$$  
  

• $$\frac{-1}{3}$$  

• $$-3$$  

Poll

Any question(s)?

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

• 16
• 4
• -4
• None of these.

Multiple Choice

f(x) = 3x + 10

g(x) = x - 2

Find g(f(-10))

• -42

• -26

• -18

• None of these.