Let f(x)=2x+5 and g(x)=4x2+3x.
After simplifying,
(f∘g)(x)= 

To find \((f \circ g)(x)\), also written as \(f(g(x))\), we substitute the expression for \(g(x)\) into \(f(x)\).

### Step 1: Write out \(f(g(x))\)
We are given:
- \(f(x) = 2x + 5\)
- \(g(x) = 4x^2 + 3x\)

Now substitute \(g(x)\) into \(f(x)\):
\[
f(g(x)) = f(4x^2 + 3x)
\]

### Step 2: Apply \(f(x) = 2x + 5\) to \(g(x)\)
To do this, replace \(x\) in \(f(x)\) with \(4x^2 + 3x\):
\[
f(g(x)) = 2(4x^2 + 3x) + 5
\]

### Step 3: Simplify the expression
Distribute the 2 across the terms inside the parentheses:
\[
f(g(x)) = 2(4x^2) + 2(3x) + 5
\]
\[
f(g(x)) = 8x^2 + 6x + 5
\]

So, the simplified form of \((f \circ g)(x)\) is:
\[
(f \circ g)(x) = 8x^2 + 6x + 5
\]

Would you like more details or have any questions?

---

Here are 5 related questions:
1. How would you compute \((g \circ f)(x)\)?
2. What is the domain of \((f \circ g)(x)\)?
3. Can you graph the function \((f \circ g)(x)\)?
4. How do the graphs of \(f(x)\) and \(g(x)\) differ?
5. What happens if \(f(x)\) is a constant function instead?

**Tip:** When composing functions, always carefully substitute one function into the other and simplify step by step.

Let f(x)=2x+5 and g(x)=4x^2+3x. After simplifying, (f∘g)(x)=

Explore the process of simplifying the function composition (f∘g)(x), where f(x)=2x+5 and g(x)=4x^2+3x. This algebra problem focuses on function composition, substitution, and polynomial simplification, 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