r(×)=×+5, q(×)=2×²-5: find q(r(-2)).

We are given two functions:

- \( r(x) = x + 5 \)
- \( q(x) = 2x^2 - 5 \)

We need to find \( q(r(-2)) \), which means we will first evaluate \( r(-2) \), and then use that result as the input for the function \( q \).

### Step 1: Find \( r(-2) \)
Substitute \( x = -2 \) into the function \( r(x) \):
\[
r(-2) = (-2) + 5 = 3
\]

### Step 2: Find \( q(3) \)
Now, substitute \( x = 3 \) into the function \( q(x) \):
\[
q(3) = 2(3)^2 - 5 = 2(9) - 5 = 18 - 5 = 13
\]

### Final Answer:
Thus, \( q(r(-2)) = 13 \).

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. What is \( q(r(x)) \) in general form?
2. How would the result change if \( r(x) = x - 5 \) instead?
3. Can you find \( q(r(0)) \)?
4. What is the domain of the composite function \( q(r(x)) \)?
5. How would you express \( r(q(x)) \) and solve for \( x = -2 \)?

**Tip:** Always check the order of operations in composite functions to avoid errors.

Learn how to solve composite functions with a detailed solution to the problem q(r(-2)) where r(x) = x + 5 and q(x) = 2x² - 5. This problem covers key algebraic concepts such as function composition and quadratic functions, suitable for students in Grades 9-10.

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