To solve this problem, we're going to evaluate [tex]\((m \circ n)(x)\)[/tex] where [tex]\( n(x) = x \)[/tex] for [tex]\( x = -3 \)[/tex] using the provided information about the functions, and then consider the incomplete part of the problem.
### Step-by-Step Solution:
1. Define the functions:
- [tex]\( n(x) = x \)[/tex]
- Assume [tex]\( m(x) = 4x + 9 \)[/tex]
2. Understanding the composition [tex]\((m \circ n)(x)\)[/tex]:
- Composition of functions means to apply one function to the result of another function.
- [tex]\((m \circ n)(x)\)[/tex] is defined as [tex]\( m(n(x)) \)[/tex].
3. Substitute [tex]\( n(x) \)[/tex] into [tex]\( m(x) \)[/tex]:
- Since [tex]\( n(x) = x \)[/tex], we need to compute [tex]\( m(n(-3)) \)[/tex].
- First, evaluate [tex]\( n(-3) \)[/tex]:
[tex]\[
n(-3) = -3
\][/tex]
4. Evaluate [tex]\( m \)[/tex] at [tex]\( n(-3) \)[/tex]:
- Next, apply [tex]\( m \)[/tex] to the result of [tex]\( n(-3) \)[/tex]:
[tex]\[
m(-3) = 4(-3) + 9
\][/tex]
[tex]\[
m(-3) = -12 + 9
\][/tex]
[tex]\[
m(-3) = -3
\][/tex]
Therefore, [tex]\((m \circ n)(-3) = -3\)[/tex].
5. The second part of the question involves [tex]\(\frac{m}{n}(x)\)[/tex]:
- However, the information provided is incomplete and we only have the expression [tex]\(\frac{m}{n}(x), x \neq \ \square \)[/tex].
- To further complete this part, additional information on [tex]\( m(x) \)[/tex] and the constraint on [tex]\( x \)[/tex] is required.
In conclusion, the evaluated result for [tex]\((m \circ n)(-3)\)[/tex] is:
[tex]\[
(m \circ n)(-3) = -3
\][/tex]
