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We are given two functions:

\[
q(x) = -x + 1
\]
and
\[
r(x) = x^2 - 1.
\]

We are asked to find the value of \( r(q(2)) \). 

Let's break this down step by step.

### Step 1: Calculate \( q(2) \)
Substitute \( x = 2 \) into the function \( q(x) \):
\[
q(2) = -(2) + 1 = -2 + 1 = -1.
\]

### Step 2: Calculate \( r(q(2)) = r(-1) \)
Now, substitute \( x = -1 \) into the function \( r(x) \):
\[
r(-1) = (-1)^2 - 1 = 1 - 1 = 0.
\]

So, the value of \( r(q(2)) \) is \( \boxed{0} \).

Would you like more details or have any questions?

Here are some related questions for practice:
1. What is the value of \( q(r(2)) \)?
2. If \( q(x) = -x + 2 \), what would \( r(q(3)) \) be?
3. Find \( q(q(2)) \) based on the given functions.
4. How would the solution change if \( r(x) = x^2 + 1 \)?
5. Solve for \( r(q(x)) \) in general form.

**Tip:** When solving composite functions, always evaluate the inner function first, then substitute its value into the outer function.

Find the value of r(q(2)), where q(x) = -x + 1 and r(x) = x^2 - 1.

Learn how to solve the composite function r(q(2)) where q(x) = -x + 1 and r(x) = x^2 - 1. This example illustrates how to evaluate functions step by step.

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