Sure, I can help you evaluate [tex]\((m n)(x)\)[/tex] for [tex]\(x = -3\)[/tex]. Let's break it down step by step.
1. Define the functions:
- [tex]\(m(x) = x^2 + 4x\)[/tex]
- [tex]\(n(x) = x\)[/tex]
2. Determine [tex]\((m n)(x):
- \((m n)(x)\)[/tex] means applying [tex]\(n(x)\)[/tex] first and then applying [tex]\(m\)[/tex] to the result of [tex]\(n(x)\)[/tex].
- Since [tex]\(n(x) = x\)[/tex], substituting [tex]\(n(x)\)[/tex] into [tex]\(m(x)\)[/tex], we get:
[tex]\[
(m n)(x) = m(n(x)) = m(x)
\][/tex]
- Therefore, [tex]\((m n)(x) = x^2 + 4x\)[/tex], as [tex]\(m(x)\)[/tex] itself.
3. Evaluate [tex]\((m n)(-3)\)[/tex]:
- First, substitute [tex]\(x = -3\)[/tex] into [tex]\(m(x)\)[/tex]:
[tex]\[
m(-3) = (-3)^2 + 4(-3)
\][/tex]
- Calculate the terms:
[tex]\[
(-3)^2 = 9
\][/tex]
[tex]\[
4(-3) = -12
\][/tex]
4. Combine the results:
- Add the terms together to get:
[tex]\[
m(-3) = 9 - 12 = -3
\][/tex]
- So, [tex]\((m n)(-3) = m(-3) = -3\)[/tex].
Therefore, the evaluation of [tex]\((m n)(-3)\)[/tex] is:
[tex]\[
(m n)(-3) = -3
\][/tex]
