Math Problem Statement

What does f(g(x)) represent in function composition?

Solution

The question asks, "What does f(g(x))f(g(x)) represent in function composition?"

The correct answer is:

a. Function ff is composed of function gg

In this context, f(g(x))f(g(x)) means you first apply function gg to xx, and then apply function ff to the result of g(x)g(x). This is known as composition of functions.

Let me know if you need more details or have any questions.

Here are five related questions to expand on this topic:

  1. How do you compute f(g(x))f(g(x)) if f(x)=x2f(x) = x^2 and g(x)=x+1g(x) = x + 1?
  2. What is the difference between function composition and addition of functions?
  3. Can function composition be commutative? Why or why not?
  4. How do you decompose a function into two simpler functions?
  5. How would you graph the composition of two functions?

Tip: When composing functions, always apply the inner function (the one inside the parentheses) first, then the outer function.

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Math Problem Analysis

Mathematical Concepts

Function Composition
Algebra

Formulas

f(g(x))

Theorems

Function Composition Theorem

Suitable Grade Level

Grades 9-12