To find \( A \), we need more context on what \( A \) represents. However, I'll assume you're asking for the composition of the functions \( F(x) \) and \( G(x) \), denoted as \( A = (F \circ G)(x) \). This means we first apply \( G(x) \), then apply \( F(x) \) to the result of \( G(x) \).

Let's calculate \( (F \circ G)(x) \):

### Step-by-step:
1. Start with \( G(x) = x + 1 \).
2. Apply this as the input to \( F(x) = 3 - x^2 \).

So, we calculate \( F(G(x)) \):

\[
F(G(x)) = F(x + 1) = 3 - (x + 1)^2
\]

Now, expand \( (x + 1)^2 \):

\[
(x + 1)^2 = x^2 + 2x + 1
\]

Substitute this back into \( F(x) \):

\[
F(G(x)) = 3 - (x^2 + 2x + 1) = 3 - x^2 - 2x - 1
\]

Simplify the expression:

\[
F(G(x)) = 2 - x^2 - 2x
\]

Thus, the composition \( (F \circ G)(x) = 2 - x^2 - 2x \).

### Conclusion:
If \( A \) is meant to represent \( (F \circ G)(x) \), then:

\[
A = 2 - x^2 - 2x
\]

Let me know if this is what you intended, or if you had a different meaning for \( A \).

---

Would you like more details or have any questions?

Here are 5 related questions:
1. What is \( G(F(x)) \) for the same functions?
2. How would you find the inverse of \( G(x) \)?
3. What is the vertex of \( F(x) \)?
4. What is the domain and range of \( F(x) \)?
5. How do we solve for \( x \) if \( F(x) = G(x) \)?

**Tip:** When composing functions, make sure to substitute carefully, especially when squaring binomials like \( (x+1)^2 \).

Learn how to compose functions F(x) = 3 - x² and G(x) = x + 1 with a step-by-step solution. This problem covers important algebraic concepts, such as function composition and quadratic functions, suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation