https://file.aiquickdraw.com/mathbot/file/172649604157791lrnfms.jpg

The given functions are:

\[
F(u) = u + 2
\]
\[
h(u) = u^2 - 3
\]

You are asked to find \((F \circ h)(u)\), which is the composition of the functions \(F\) and \(h\). This means we need to substitute \(h(u)\) into \(F(u)\).

1. First, substitute \(h(u)\) into \(F(u)\):
\[
(F \circ h)(u) = F(h(u)) = F(u^2 - 3)
\]

2. Now, use the expression for \(F(u)\), which is \(F(u) = u + 2\). Substitute \(u^2 - 3\) in place of \(u\):
\[
F(u^2 - 3) = (u^2 - 3) + 2
\]

3. Simplify the expression:
\[
F(u^2 - 3) = u^2 - 3 + 2 = u^2 - 1
\]

Thus, \((F \circ h)(u) = u^2 - 1\).

Let me know if you'd like further details or explanations!

Here are five related questions to explore this further:
1. How do you compute the composition of functions in general?
2. What are the conditions for the composition of two functions to exist?
3. How do you graph the composition of two functions?
4. What happens if the order of composition is reversed, i.e., \( (h \circ F)(u) \)?
5. Can function composition be applied to functions with multiple variables?

**Tip:** When solving compositions of functions, always start by substituting the inner function into the outer function and then simplify the result.

Given F(u) = u + 2 and h(u) = u^2 - 3, find (F ∘ h)(u).

Learn how to solve a function composition problem with F(u) = u + 2 and h(u) = u^2 - 3. The step-by-step solution explains key algebraic concepts and how to compute (F ∘ h)(u). Suitable for high school students in grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation