Add, Subtract, Multiply and Divide Functions

Definition: Functions can be added, subtracted, multiplied and divided.
The following notation is used to express these operations:

Addition:
(f + g)(x) = f(x) + g(x)

Subtraction:
(f – g)(x) = f(x) – g(x)

Multiplication:
(fg)(x) = f(x) * g(x)

Divison:
(f/g)(x) = f(x) / g(x)

Composition:
(f ◦ g)(x) = “f of g of x” = f(g(x))

Example: Given f(x) = 6x and g(x) = x + 8, find (f/g)(4)

Solution:

Step 1: Here we are given f(x) = 6x and g(x) = x + 8, so to find (f/g)(4) we’ll first follow the rule for dividing functions:

f/g(x) = f(x) / g(x)
f(x)/g(x) = 6x / x+8

Step 2: In this problem, we are evaluating for x = 4, so can plug in 4 wherever we see x:

f/g(x) = 6x / x + 8
f/g(4) = 6(4) / (4 + 8)

Simplify to solve:

f/g(4) = 24 / 12 = 2

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