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To solve question 33, we are given the functions:

- \( f(x) = x + 2 \)
- \( g(x) = -4x + 3 \)
- \( h(x) = x^2 - 2x + 1 \)

We need to evaluate:

\[
(f \cdot g \cdot h)(3)
\]

This represents the product of the values of \( f(3) \), \( g(3) \), and \( h(3) \).

### Step 1: Calculate \( f(3) \)
Using \( f(x) = x + 2 \), substitute \( x = 3 \):

\[
f(3) = 3 + 2 = 5
\]

### Step 2: Calculate \( g(3) \)
Using \( g(x) = -4x + 3 \), substitute \( x = 3 \):

\[
g(3) = -4(3) + 3 = -12 + 3 = -9
\]

### Step 3: Calculate \( h(3) \)
Using \( h(x) = x^2 - 2x + 1 \), substitute \( x = 3 \):

\[
h(3) = 3^2 - 2(3) + 1 = 9 - 6 + 1 = 4
\]

### Step 4: Calculate the product
Now, multiply the results:

\[
(f \cdot g \cdot h)(3) = f(3) \cdot g(3) \cdot h(3) = 5 \cdot (-9) \cdot 4
\]

\[
= -45 \cdot 4 = -180
\]

Thus, the value of \( (f \cdot g \cdot h)(3) \) is \( \boxed{-180} \).

---

Would you like further details on any of the steps? Here are five related questions you might want to consider:

1. How do you find compositions of functions, such as \( (f \circ g)(x) \)?
2. How would the process change if we had to evaluate \( (f + g + h)(3) \)?
3. What are the interpretations of function operations like addition, subtraction, and division?
4. Can functions have multiple types of compositions, and how do they differ?
5. How do transformations of basic functions affect their graphs?

**Tip:** When performing multiple function operations, be sure to calculate each individual function value before applying operations like multiplication or addition.

Solve the problem (f · g · h)(3) where f(x) = x + 2, g(x) = -4x + 3, h(x) = x^2 - 2x + 1.

Learn how to solve the function multiplication problem (f · g · h)(3) using the functions f(x) = x + 2, g(x) = -4x + 3, and h(x) = x^2 - 2x + 1. This solution provides step-by-step calculations for each function value and the final result. Suitable for students in Grades 10-12.

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