Appendix
A-8: Functions
Example A-8.3
If , obtain the composition . What is the domain of this composition?
Solution
Interactive Solution
Type the equation
Context Panel: Assign Function
Type the required composition.
Context Panel: Evaluate and Display Inline
Context Panel: Simplify≻Simplify
=
Define the composition as a new function
The domain of is the set of real numbers except for . The rule for the composition is undefined for . Hence, the domain for the composition is the set of real numbers except for .
Coded Solution
Define the function as shown to the right.
Apply simplify to the composition.
Define the composite function with the "@" symbol.
The mathematical notation for the composition of the functions f and g is . Maple uses @, the "at" symbol, for "∘" because it's the closest thing to it on the keyboard.
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