Math Problem Statement

(f∘g)(3)

Solution

The image shows the mathematical expression (fg)(3)(f \circ g)(3), which represents the composition of two functions, ff and gg, evaluated at 33.

To proceed with solving the expression, I need the definitions of the functions f(x)f(x) and g(x)g(x). Could you please provide those functions, or clarify if they are given elsewhere?

Let me know if you'd like to explore more about function compositions or related concepts!

Here are some questions for further exploration:

  1. How do you generally compose functions f(g(x))f(g(x))?
  2. What happens if you reverse the composition order, i.e., (gf)(x)(g \circ f)(x)?
  3. How do you interpret function compositions graphically?
  4. What are common uses of function compositions in real-world applications?
  5. How does domain and range affect the composition of two functions?

Tip: Always verify that the output of g(x)g(x) lies within the domain of f(x)f(x) when composing functions!

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Math Problem Analysis

Mathematical Concepts

Function Composition
Evaluating Functions

Formulas

(f∘g)(x) = f(g(x))

Theorems

Function Composition Theorem

Suitable Grade Level

Grades 9-11