Function Notation

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(f+g)(x)--> add equations
(f-g)(x)--> subtract equations
(f.g)(x)--> multiply equations
(f/g)(x)--> divide
(fog)(x) or f(g(x))--> replace all x's in the f(x) equation with the equation g(x)
--If x is replaced with a number plug into the equation

Example 1:
Let f(x)=x^2+x and g(x)=x+1. Find each of the following.
(f+g)(x)
(x^2+x)+(x+1)
x(x+1)+(x+1)
x(x+1)^2

Example 2:
Let f(x)=x^2+x and g(x)=x+1. Find each of the following.
(f-g)(x)
(x^2+x)-(x+1)
x(x+1)-(x+1)

Example 3:
Let f(x)=x^2+x and g(x)=x+1. Find each of the following.
(f.g)(x)
(x^2+x)(x+1)
x^3+x^2+x^2+1
x^4+x^3+1

Example 4:
Let f(x)=x^2+x and g(x)=x+1. Find each of the following.
(f/g)(x)
x^2+x/x+1=x(x+1)/(x+1)
**The x+1's cancel, you are left with x
=x

Example 5:
Let f(x)=x^2+x and g(x)=x+1. Find each of the following.
(fog)(x)
(x+1)^2+x+1
x^2+2+x+1
x^2+x+3

Example 6:
Find each of the following.
a. (f+g)(0)
f(x)=square root of 25-x^2= square root of 25-0^2 +absolute value of 0=5
g(x)=absolute value of x
b. (f+g)(3)
f(x)=square root of 25-x^2=square root of 25-3^2 +absolute value of 3= 4+3
4+3=7 4-3=1