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