Problem 106 - College Algebra Essentials

Question

Describe a procedure for finding \((f \circ g)(x) .\) What is the name of this function?

Step-by-Step Solution

Answer

The procedure involves applying function g to the input first, then applying function f to the result of g(x). The resultant function is commonly known as function composition, or 'f compose g of x'.

Step 1: Understand Function Composition

Understand that function composition \((f \circ g)(x)\) is a concept that the output from the g function is the input for the f function. Essentially, this means first applying g to the input x (giving g(x)), and then applying f to the result (giving f(g(x))).

Step 2: Procedure to Find Function Composition

To find \((f \circ g)(x)\), start with the rightmost function, which in this case is g. Apply the function g to the input variable x, yielding an output g(x). Now, apply the function f to the output of the first function, or f(g(x)). This result is the composition of function f and g.

Step 3: Provide Name of Function

The operation \((f \circ g)(x)\) is known as function composition, or more simply, the composition of f and g. The resultant function can also be referred to as 'f compose g of x'.