Composition of Functions

Composition of Functions.

• Objectives:

• Create a new function by composition of functions

• ​Evaluate composite functions​

Multiple Choice

Review:

For the function $$f\left(x\right)=4x^2-2$$

find f(-2)

• 2

• -2

• 0

• 14

Multiple Choice

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

• 2

• 15

• 7

• -9

Multiple Choice

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

• $$\frac{1}{4}$$  

• $$\frac{1}{8}$$  

• $$\frac{7}{2}$$  

• 8

Multiple Choice

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

• $$\frac{1}{4}$$  

• $$1$$

• $$-1$$  

• $$-\frac{1}{4}$$  

Multiple Choice

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

• 2

• 15

• 7

• -9

Fill in the Blank

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$f\left(g\left(3\right)\right)$$  

Multiple Choice

Let

f(x) = 3x + 10

g(x) = x - 2

h(x) = 4x - 5

Evaluate h(f(g(2))

• 16

• 45

• 35

• None of these.

-The process of combining functions so that the output of one function becomes the input of another is known as a composition of functions.

-The resulting function is known as a composite function​

Composition of Functions

Multiple Choice

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

• $$4x^2-1$$  

• $$4x^2-2$$  

• $$8x^2-1$$  

• $$16x^2-1$$  

Multiple Choice

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

• $$4x^2-1$$  

• $$4x^2-2$$  

• $$8x^2-1$$  

• $$16x^2-1$$  

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(x) = x-1 and g(x) = 2x,

what is and g(f(x)) ?

• 2x²-1

• 2x-1

• 2x-2

• x-2

Multiple Choice

If $$g\left(x\right)=x^2+6$$   and $$f\left(x\right)=2x-4$$  , find $$g\left(f\left(x\right)\right)$$  

• $$2x^2-12x-4$$  

• $$2x^2+12x-4$$  

• $$4x^2-16x+22$$  

• $$x^3-2x^2+1$$  

Multiple Choice

If $$g\left(x\right)=x^2+6$$   and $$f\left(x\right)=2x-4$$  , find f(g(x))

• $$2x^2-12x-4$$  

• $$2x^2+8$$  

• $$4x^2-16x+22$$  

• $$x^3-2x^2+1$$