Math Problem Statement

(f ◦ g)(x)

Solution

To compute (fg)(x)(f \circ g)(x), also known as the composition of functions ff and gg, it means you are plugging the output of g(x)g(x) into the function f(x)f(x). In other words, (fg)(x)=f(g(x))(f \circ g)(x) = f(g(x)).

For example, if you have:

  • f(x)=2x+3f(x) = 2x + 3
  • g(x)=x2+1g(x) = x^2 + 1

Then: (fg)(x)=f(g(x))=f(x2+1)=2(x2+1)+3=2x2+2+3=2x2+5(f \circ g)(x) = f(g(x)) = f(x^2 + 1) = 2(x^2 + 1) + 3 = 2x^2 + 2 + 3 = 2x^2 + 5

Would you like to share the specific functions for f(x)f(x) and g(x)g(x), so we can find the exact composition for your case?

Here are 5 related questions to expand on this:

  1. How do you find the domain of a composition of functions?
  2. Can you reverse the composition and compute (gf)(x)(g \circ f)(x)?
  3. What is the difference between function composition and multiplication?
  4. What happens if f(x)f(x) and g(x)g(x) are inverse functions?
  5. How does the composition of functions relate to real-world problems?

Tip: Always check if both f(x)f(x) and g(x)g(x) are defined for the given input when computing compositions!

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Math Problem Analysis

Mathematical Concepts

Function Composition
Algebra

Formulas

(f ◦ g)(x) = f(g(x))
f(x) = 2x + 3
g(x) = x^2 + 1

Theorems

Function Composition Theorem

Suitable Grade Level

Grades 9-12