2.7 Composition of Functions

Unit 2: Functions and their Graphs

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​2.7 Composition of Functions

Remember to date and title your name.​

1. Vocabulary

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Draw

Show your work and your answer on the screen below.

Multiple Choice

• $$\left(h\circ g\right)\left(x\right)=2x$$  

• $$\left(h\circ g\right)\left(x\right)=\frac{1}{2x}$$  

• $$\left(h\circ g\right)\left(x\right)=\frac{2x}{x}$$  

• $$\left(h\circ g\right)\left(x\right)=\frac{1}{x}$$  

Multiple Choice

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$g\left(f\left(x\right)\right)$$  

• $$4x^2-1$$  

• $$4x^2-2$$  

• $$8x^2-1$$  

• $$16x^2-1$$  

Multiple Choice

If $$f\left(x\right)=\frac{1}{x}$$   and  $$g\left(x\right)=3x+2$$   find $$\left(g\circ f\right)\left(x\right)$$  

• $$\frac{1}{3x}+2$$

• $$3x+2$$  

• $$\frac{3}{x}+2$$  

• $$\frac{1}{3x+2}$$  

Multiple Choice

If $$f\left(x\right)=\frac{1}{x}$$   and  $$g\left(x\right)=3x+2$$   find $$f\left(g\left(x\right)\right)$$  

• $$\frac{1}{3x}+2$$

• $$3x+2$$  

• $$\frac{3}{x}+2$$  

• $$\frac{1}{3x+2}$$  

Multiple Choice

If $$f\left(x\right)=x^2$$   and  $$g\left(x\right)=\frac{1}{x^2}$$   find $$\left(f\circ g\right)\left(-1\right)$$  

• $$\frac{1}{4}$$  

• $$1$$

• $$-1$$  

• $$-\frac{1}{4}$$  

​The domain of the composite function   is

​the domain of g such that g(x) in the domain of f.

​https://www.desmos.com/calculator/0jwb7onjrb

Open Ended

What will be the domain of the function $$\left(f\circ g\right)\left(x\right)$$   if $$f\left(x\right)=3x^2$$   and $$g\left(x\right)=\frac{1}{x}$$  ?