https://file.aiquickdraw.com/mathbot/file/1727568896274yugsfl4l.jpg

The image provides two functions:

\[
f(x) = 4x - 14
\]
\[
g(x) = x^2 - 4x - 3
\]

We are asked to find \( f(g(x)) \), which is the composition of the functions \( f \) and \( g \). This means we will substitute \( g(x) \) into \( f(x) \).

### Steps to find \( f(g(x)) \):
1. Start by substituting \( g(x) = x^2 - 4x - 3 \) into \( f(x) = 4x - 14 \).
   
   So, \( f(g(x)) = f(x^2 - 4x - 3) \).

2. Apply the function \( f \) to \( g(x) \):
   
   \[
   f(g(x)) = 4(x^2 - 4x - 3) - 14
   \]

3. Now, distribute the 4 inside the parentheses:

   \[
   f(g(x)) = 4x^2 - 16x - 12 - 14
   \]

4. Combine like terms:

   \[
   f(g(x)) = 4x^2 - 16x - 26
   \]

So, the composition \( f(g(x)) \) is:

\[
f(g(x)) = 4x^2 - 16x - 26
\]

Would you like further details or clarifications on any part of this solution?

### Related Questions:
1. What is the composition \( g(f(x)) \) using the same functions?
2. How would you solve \( f(g(x)) = 0 \)?
3. Can you find the inverse of \( f(x) \) or \( g(x) \)?
4. What are the roots of \( g(x) = 0 \)?
5. What does the graph of \( f(g(x)) \) look like?

### Tip:
When composing functions, make sure to replace the entire input variable in the outer function with the inner function's expression.

Find the composition f(g(x)) where f(x) = 4x - 14 and g(x) = x^2 - 4x - 3.

Learn how to find the composition of functions f(x) = 4x - 14 and g(x) = x^2 - 4x - 3, resulting in the quadratic expression f(g(x)) = 4x^2 - 16x - 26. This problem demonstrates the concept of function composition and is suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation