https://file.aiquickdraw.com/mathbot/file/17265278856685xcadozb.jpg

In the image, the given functions are:

\[
F(\psi) = \psi + 2
\]
\[
h(\psi) = \psi^2 - 3
\]
The question asks for \((f \circ h)(\psi)\), which is the composition of the two functions.

To solve for \((f \circ h)(\psi)\), we need to substitute \(h(\psi)\) into \(F(\psi)\). Here's the process:

### Step 1: Start with \(h(\psi)\)
\[
h(\psi) = \psi^2 - 3
\]

### Step 2: Substitute \(h(\psi)\) into \(F(\psi)\)
Since \(F(\psi)\) is defined as \(\psi + 2\), we replace \(\psi\) with \(h(\psi)\):

\[
F(h(\psi)) = h(\psi) + 2
\]

### Step 3: Simplify the expression
Substitute \(h(\psi) = \psi^2 - 3\) into the above expression:

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

\[
F(h(\psi)) = \psi^2 - 1
\]

### Final Answer:
\[
(f \circ h)(\psi) = \psi^2 - 1
\]

Let me know if you would like further details or clarifications.

---

Here are five related questions you could explore:
1. What is the inverse of \(F(\psi) = \psi + 2\)?
2. How do you find the inverse of a composite function?
3. What happens when you compose \(h(\psi)\) with \(F(\psi)\)?
4. How does function composition relate to transformations in geometry?
5. Can you express a general rule for composing two functions?

**Tip:** When composing functions, always substitute the inner function into the outer function carefully to avoid mistakes.

What is (f of h)(ψ) given that F(ψ) = ψ + 2 and h(ψ) = ψ^2 - 3?

Learn how to solve the function composition (f of h)(ψ) where F(ψ) = ψ + 2 and h(ψ) = ψ^2 - 3. This example demonstrates key algebraic concepts related to function composition and quadratic functions. Perfect for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation