Composition of Functions Day 1

Composition of Functions Day 1

Feb 8, 2021

Composition of Functions

• Notation:

   $f\left(g\left(x\right)\right)$  

• said "f of g of x"

• Always work from the inside out

• Evaluate the inner function  $g\left(x\right)$  

• Plug that value in to the next function  $f\left(x\right)$  

• Then solve for  $f\left(x\right)$  

• Write your answer as  $f\left(g\left(x\right)\right)=$  ____

 $f\left(16\right)=27$   $f\left(x\right)=2x-5$  and  $g\left(x\right)=x^2-6x$  

• Find  $f\left(g\left(-2\right)\right)$  

• Evaluate  $g\left(-2\right)$  

•  $g\left(-2\right)=\left(-2\right)^2-6\left(-2\right)$  

•  $g\left(-2\right)=16$  

• Plug 16 into f(x) and solve

•  $f\left(16\right)=2\left(16\right)-5$  

• Write your final answer as  $f\left(g\left(x\right)\right)=27$  

Open Ended

Given:

 $f\left(x\right)=2x-15$   $g\left(x\right)=x^2-6x$   $h\left(x\right)=2x^2+5x-3$  

Find:  $g\left(f\left(1\right)\right)$  

Open Ended

Given:

 $f\left(x\right)=2x-15$   $g\left(x\right)=x^2-6x$   $h\left(x\right)=2x^2+5x-3$  

Find:  $h\left(f\left(3\right)\right)$  

Open Ended

Given:

 $f\left(x\right)=2x-15$   $g\left(x\right)=x^2-6x$   $h\left(x\right)=2x^2+5x-3$  

Find:  $g\left(h\left(-3\right)\right)$  

Open Ended

Given:

 $f\left(x\right)=2x-15$   $g\left(x\right)=x^2-6x$   $h\left(x\right)=2x^2+5x-3$  

Find:  $f\left(h\left(4\right)\right)$