Arithmetic Combinations of Functions
Just like two real numbers, functions can be combined by the operations of addition, subtraction, multiplication, and division.
Definitions:
Examples:
and 
, find the sum, difference, product, and quotient of f and g.Sum:
Difference:
Product:
Quotient:
Compositions of Functions
Another way of combining two functions is to form the composition of one with the other.
Definition:
The composition of the function f with g is 
.
.The domain of 
is the set of all x in the domain of g such that g(x) is in the domain of f.
is the set of all x in the domain of g such that g(x) is in the domain of f.Example:
Find 
for 
and 
. If possible, find 
and 
.
for 
and 
. If possible, find 
and 
.
The domain of is [1, ∞). So = 
is defined, but is not defined because 0 is not in the domain of .
is [1, ∞). So = is defined, but is not defined because 0 is not in the domain of .
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