To find \((b \circ a)(x)\), which is the composition of the two functions \(b(x)\) and \(a(x)\), follow these steps:

1. The composition \((b \circ a)(x)\) means plugging the function \(a(x)\) into the function \(b(x)\).
2. Since \(a(x) = x + 2\), substitute \(a(x)\) into \(b(x)\).
3. The function \(b(x)\) is \(b(x) = 7x^2\), so replace \(x\) in \(b(x)\) with \(a(x)\):
   \[
   (b \circ a)(x) = b(a(x)) = 7(a(x))^2 = 7(x + 2)^2
   \]
4. Now, expand \((x + 2)^2\):
   \[
   (x + 2)^2 = x^2 + 4x + 4
   \]
5. Multiply by 7:
   \[
   (b \circ a)(x) = 7(x^2 + 4x + 4) = 7x^2 + 28x + 28
   \]

Thus, \((b \circ a)(x) = 7x^2 + 28x + 28\).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the composition of two linear functions?
2. How does composition differ from simple function multiplication?
3. How do you find the inverse of a composite function?
4. How does the order of composition affect the outcome?
5. Can you always compose two functions?

**Tip:** In function composition, the order matters! \( (b \circ a)(x) \neq (a \circ b)(x) \).

Explore the solution to the composition of functions problem where a(x) = x + 2 and b(x) = 7x^2. Learn how to substitute and expand (x + 2)^2 step-by-step, resulting in (b ∘ a)(x) = 7x^2 + 28x + 28. Suitable for students in Grades 9-10.

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