Comp Real Fn
Comp Real Fn is a direct subtype of Real To Real Function
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TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE Comp Real Fn
This type represents a function ƒ that represents the composite of the given r constituent functions ƒ₁, ƒ₂, ..., ƒᵣ
Using the conventional mathematical symbol ⸰ for the composition operator between functions, the formal definition is:
ƒ = ƒᵣ ⸰ ... ⸰ ƒ₂ ⸰ ƒ₁
Any point p in the domain of the first function ƒ₁ is mapped consecutively to its final value y as follows:
p -> ƒ₁(p) -> ƒ₂(ƒ₁(p)) -> ... -> ƒᵣ(ƒᵣ₋₁(...ƒ₁(p)...)) = y
As an example, below is the chart of a Comp Real Fn function composed of two single-variable functions.
On the input variable x acts first a linear function ƒ defined as ƒ(x) = x - 1
The chart of ƒ is depicted as a straight line that cuts the vertical axis at -1
A better way of viewing the action of ƒ is that it shifts any given point on the x axis with value x to the left by one unit.
Then on the output of ƒ acts a quadratic function - special case of the more general power function - with defining formula 𝘨(x) = x²
The composite function is denoted as 𝘨 ⸰ ƒ and it is defined by the formula (𝘨 ⸰ ƒ)(x) = 𝘨( ƒ(x) )
Replacing from above one gets: (𝘨 ⸰ ƒ)(x) = 𝘨(x - 1) = (x - 1)²
