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Compositions of Functions

When the variable name in a function is replaced with another function, the result is called a composite function. If




then f [ g( x)] is a composite function. The statement f[ g( x)] is read “ f of g of x” or “the composition of f with g.” f [ g( x)] can also be written as




The symbol between f and g is a small open circle.

Example 1: If f ( x) = 3 x + 2 and g( x) = 4 x − 5, find each of the following.




From the previous example, notice that f[ g( x)] and g[ f( x)] are not equal.

Example 2: If f( x) = 3 x2 + 2 x + 1 and g( x) = 4 x − 5, find each of the following.




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