Math Problem Statement

(fog)(x)

Solution

The notation (fg)(x)(f \circ g)(x), or (fg)(x)(f \circ g)(x), refers to the composition of two functions ff and gg. The composition of ff and gg is written as f(g(x))f(g(x)), meaning that you first apply gg to xx, and then apply ff to the result of g(x)g(x).

If you are asking about the composition (fg)(x)(f \circ g)(x), here’s the general process:

  1. Evaluate g(x)g(x): Plug the value of xx into the function gg.
  2. Apply ff to g(x)g(x): Take the result from g(x)g(x) and substitute it into the function ff.

So, (fg)(x)=f(g(x))(f \circ g)(x) = f(g(x)).

Would you like an example with specific functions for more clarity? Or do you need a breakdown of how to calculate it?


Here are some related questions that expand on this topic:

  1. How do you find the domain of a composition of functions?
  2. What is the inverse of a function composition?
  3. How do you handle compositions of three or more functions?
  4. How do compositions behave with trigonometric functions?
  5. How can function composition be used in calculus (e.g., in chain rule)?

Tip: Make sure that the range of the inner function g(x)g(x) is within the domain of the outer function ff when composing functions.

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Math Problem Analysis

Mathematical Concepts

Function composition
Evaluation of functions

Formulas

(f ∘ g)(x) = f(g(x))

Theorems

Domain and range compatibility for function composition

Suitable Grade Level

Grades 9-12