Operations of Functions

Operations of Functions

By Kayley Fuller

Operations of Functions

​Addition of Functions

f(x)=3x+1 g(x)=4x-10

f(x)+g(x)= (f +g)(x)= (3x+1) + (4x-10) = 7x-9

Combine all like terms!

Operations of Functions

​Subtraction of Functions

f(x)=3x+1 g(x)=4x-10

f(x)-g(x)= (f -g)(x)= (3x+1) - (4x-10) = 3x+1 -4x +10= -x+11

Distribute the negative through g(x), and combine like terms

Operations of Functions

​Multiplicaiton of Functions

Use a box or FOIL, and combine like terms

Multiple Choice

When adding functions, select what best describes what you do.

• FOIL

• distribute the negative sign

• combine like terms

• you can't

Multiple Choice

$$f\left(x\right)=4x+1$$   and $$g\left(x\right)=12x^2-10x+1$$  .

Find $$f\left(x\right)+g\left(x\right)$$  

• $$12x^2-6x+2$$  

• $$12x^2-14x+2$$  

• $$12x^2+14x+2$$  

• $$12x^2+6x+2$$  

Multiple Choice

$$f\left(x\right)=3x^2-10x+1$$   and $$g\left(x\right)=x^{2\ }-9x+1$$  

Find $$\left(f-g\right)\left(x\right)$$  

• $$4x^2+8x-1$$  

• $$2x^2-x$$  

Operations of Functions

Composition of Functions

​A composition function is going to be a function within another function.

Composition of Functions Video ​

Click on the link above​

https://www.youtube.com/watch?v=Clsaq_GytpA 

Operations of Functions

Steps for Composite functions:

1) substitute input function into outside function

2) ​Replace x with input function

3) fully simplify​

​Find f(g(x)):