https://file.aiquickdraw.com/mathbot/file/1727286776411cqjocc3v.jpg

The problem asks to find \( f(g(x)) \), where the functions are defined as:

\[
f(x) = 4 + 5x
\]
\[
g(x) = 2x - 1
\]

To find \( f(g(x)) \), substitute \( g(x) = 2x - 1 \) into \( f(x) \):

\[
f(g(x)) = f(2x - 1)
\]

Now, replace \( x \) in the function \( f(x) = 4 + 5x \) with \( 2x - 1 \):

\[
f(2x - 1) = 4 + 5(2x - 1)
\]

Simplify:

\[
f(2x - 1) = 4 + 5(2x) - 5(1)
\]
\[
f(2x - 1) = 4 + 10x - 5
\]
\[
f(2x - 1) = 10x - 1
\]

So, \( f(g(x)) = 10x - 1 \).

The correct answer is:

\(\boxed{10x - 1}\).

Do you want further details or have any other questions?

Here are 5 related questions:
1. How do you evaluate composite functions in general?
2. What are the common mistakes in solving \( f(g(x)) \)?
3. How do you interpret composite functions graphically?
4. Can composite functions be reversed? How?
5. What are real-world applications of composite functions?

**Tip:** Always ensure you substitute the inner function correctly when solving composite functions.

f(x) = 4 + 5x, g(x) = 2x - 1. Find f(g(x)).

Learn how to solve composite function f(g(x)) where f(x) = 4 + 5x and g(x) = 2x - 1. This detailed solution involves substituting g(x) into f(x) and simplifying the equation. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation