Operations of functions

From Math Wiki

Say you have two functions: f(x)=2x-4, and g(x)=-4x+3

Adding functions: To add functions you put an addition sign between the two functions, and then add like terms.

• For example: f(x)+g(x): 2x-4+-4x+3
• Then you add like terms: 2x-4x, and -4+3
• This gives you -2x-1, so f(x)+g(x)=-2x-1

Subtracting Functions: This is a little trickier

steps:

1. Separate the functions by putting them in paranthesis
2. Distribute the negative sign
3. Combine like terms

Take for example f(x)-g(x)

• (2x-4)-(-4x+3), then distribute the negative sign
• this gives you 2x-4+4x-3. Then combine like terms
• 2x+4x, and -4-3
• So f(x)-g(x)=6x-7

Multiplying Functions: There are two different ways to do this

the easiest way to explain this is to show you through examples:

• f(x)*g(x): 2x(-4x+3)+ -4(-4x+3)
• inorder to solve this you need to distribute the f(x) equation to the g(x) equation and add them together:
• -8x^2+6x+16x+-12
• now collect like terms:
• -8x^2+22x+-12= f(x)*g(x)

now its gets a little easier to make a mistake, but its actually very simple

Take for exapmle f(g(x))

• to sovle this problem you simply relpace the x in the f(x) equation with the g(x) equation and solve
• for istance 2(-4x+3)+3
• now all you need to do is distrubte the 2, pretty easy
• -8x+6+3
• combine like terms and you get -8x+9= f(g(x))