1.4 Combinations of Functuons
In this section you will be learning how to combine functions using Arithmetic Combinations of Functions, which are listed below.
Arithmetic Combinations of Functions
1. (f+ g)(x)= f(x)+g(x)
2. (f-g)(x)= f(x)-g(x)
3. (fg)(x)= f(x)*g(x)
4. (f/g)(x)= f(x)/g(x)
Ex. 1)Solve for all arithmetic combinations of functions when f(x)=2x+1 g(x)=x²+2x-1.
(f+g)(x)= 2x+1+x²+2x-1
(f+g)(x)= x²+4x
(f-g)(x)= 2x+1-(x²+2x-1)
(f-g)(x)= 2x+1-x²-2x+1
(f-g)(x)=-x²+2
(fg)(x)=(2x+1)(x²+2x-1)
(fg)(x)=2x³+4x²-2x+x²+2x-1
(fg)(x)=2x³+5x²-1
(f/g)(x)=
The composition of f with g: f(g(x)) or (fg)(x)
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Ex. 2) Find f(g(x)) when f(x)=x+2 and g(x)=4-x².
f(g(x))=4-x²+2
f(g(x))=-x²+6
g(f(x))=4-(x+2)²
g(f(x))=4-(x²+4x+4)
g(f(x))=4-x²-4x-4
g(f(x))=-x²-4x
Ex. 3) Find f(x)+g(x)
f(g(x))=(3x-5)³
g(x)=3x-5
f(x)=x³