We are tasked with evaluating the function:

$f(x) = \left[ (x - 2)^2 - x \right]^2$

at $x = 3$. Let's go step by step:

Step 1: Substitute $x = 3$ into the expression inside the brackets.

$f(3) = \left[ (3 - 2)^2 - 3 \right]^2$

Step 2: Simplify the expression inside the parentheses.

$(3 - 2)^2 = 1^2 = 1$

So, we have:

$f(3) = \left[ 1 - 3 \right]^2 = (-2)^2$

Step 3: Square the result.

$(-2)^2 = 4$

Thus, $f(3) = 4$.

Final Answer:

$f(3) = 4$

Would you like further details or explanations?

Here are 5 related questions:

1. How would you compute the derivative of $f(x)$?
2. What happens to $f(x)$ as $x \to 2$?
3. What is the second derivative of $f(x)$?
4. Can you sketch the graph of $f(x)$?
5. How would you find the critical points of $f(x)$?

Tip: Always simplify expressions inside parentheses or brackets first before applying further operations like squaring or taking powers.