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Chapter 2: Problem 106

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

Short Answer

Expert verified
The procedure involves evaluating the inner function \( g(x) \) at a given input then using that output as an input into the outer function \( f(x) \). The name of this operation/function is 'function composition' or 'composite function'.

Step by step solution

01

Understand the operation

The notation \((f \circ g)(x)\) stands for the composition of two functions \( f(x) \) and \( g(x) \). 'Composition' is an operation where the output of one function, \(g(x)\), becomes the input of another function, \(f(x)\).
02

Compute the composition

To find \((f \circ g)(x)\), first evaluate the inside function at a given input, \(x\), to get \(g(x)\). Then take this result and substitute it into the other function, \(f(x)\). So, the composition of \(f\) and \(g\) is defined as \((f \circ g)(x) = f(g(x))\).
03

Identify the name of the function

The name of this function is commonly called the 'composite function' because it is made up of two other functions. Thus, we have the composite of \( f \) and \( g \), denoted \((f \circ g)(x)\).

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Most popular questions from this chapter

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