Math Problem Statement

Given two functions F(x) = x^2 + x - 12 and G(x) = x - 3.

Solution

The image contains two functions:

  1. F(x)=x2+x12F(x) = x^2 + x - 12
  2. G(x)=x3G(x) = x - 3

Would you like help finding their combined operations such as composition (F(G(x))F(G(x)) or G(F(x))G(F(x))) or solving for roots, intersections, or other properties?

Let me know if you want details or have specific questions, and here are some related questions to expand:

  1. What are the roots of F(x)F(x)?
  2. What happens when you compose F(x)F(x) and G(x)G(x) (e.g., F(G(x))F(G(x)))?
  3. How do the graphs of F(x)F(x) and G(x)G(x) intersect?
  4. What is the domain and range of F(x)F(x) and G(x)G(x)?
  5. Can F(x)F(x) be factored, and what does it tell us?

Tip: When solving quadratic equations like F(x)F(x), factoring or using the quadratic formula can simplify the process.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Quadratic Equations
Composition of Functions

Formulas

F(x) = x^2 + x - 12
G(x) = x - 3
Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

Theorems

Quadratic formula

Suitable Grade Level

Grades 9-11