Appendix
A-8: Functions
Example A-8.3
If hx=1/1+x, obtain the composition hhx. What is the domain of this composition?
Solution
Maple Solution - Interactive
Type the equation hx=…
Context Panel: Assign Function
hx=1/1+x→assign as functionh
Type the required composition.
Context Panel: Evaluate and Display Inline
Context Panel: Simplify≻Simplify
hhx = 11+11+x= simplify 1+x2+x
Define the composition as a new function H
Type the equation Hx=…
Hx=hhx→assign as functionH
The domain of h is the set of real numbers except for x=−1. The rule for the composition is undefined for x=−2. Hence, the domain for the composition is the set of real numbers except for x=−1,−2.
Maple Solution - Coded
Define the function f as shown to the right.
h≔x→1/1+x
Apply simplify to the composition.
simplifyhhx
Define the composite function with the "@" symbol.
H≔h@h
The mathematical notation for the composition of the functions f and g is f∘g. Maple uses @, the "at" symbol, for "∘" because it's the closest thing to it on the keyboard.
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