1.4 Combinations of Functions

Arithmetic Combinations of Functions

Sum: (f + g)(x) = f(x) + g(x)
Difference: (f - g)(x) = f(x) - g(x)
Product: (fg)(x) = f(x) x g(x)
Quotient: (f/g)(x) = f(x)/g(x)

f(x)= 2x+1
g(x) x^2+2x-1

(f+g)(x)=f(x) + g(x)
            =(2x-1) + (x^2+2x-1)
            =x^2 + 4x

(fg)(x)= f(x)g(x)
         = (x^2)(x-3)
         = x^3 -3x^2
(fg)(4)= 4^3- 3(4)^2
         = 16

Compositions of Functions

(fog)(x)= f(g(x))

f(x)= x+2
g(x)= 4-x^2

(fog)(x)=
f(g(x))=
f(4-x^2)=
(4-x^2)+2=
-x^2+6=

A function has an inverse when you plug it into the other one ((fog)(x)) and the input "x" is the same as the output.