To solve the problem of evaluating [tex]\((m \circ n)(x)\)[/tex] for [tex]\(x = -3\)[/tex], follow these steps:
1. Understand the Given Functions:
- [tex]\(m(x) = x\)[/tex]
- [tex]\(n(x) = x\)[/tex]
2. Evaluate the Inner Function:
- Compute [tex]\(n(x)\)[/tex] for [tex]\(x = -3\)[/tex]. Since [tex]\(n(x) = x\)[/tex], substituting [tex]\(x = -3\)[/tex] gives:
[tex]\[
n(-3) = -3
\][/tex]
3. Evaluate the Outer Function:
- Now, we need to compute [tex]\(m(n(-3))\)[/tex].
- Since we previously found [tex]\(n(-3) = -3\)[/tex], we now substitute [tex]\(-3\)[/tex] into the function [tex]\(m\)[/tex].
- Given [tex]\(m(x) = x\)[/tex], substituting [tex]\(x = -3\)[/tex]:
[tex]\[
m(-3) = -3
\][/tex]
4. Combine the Results:
- Therefore, [tex]\((m \circ n)(-3)\)[/tex] or [tex]\(m(n(-3)) = -3\)[/tex].
So, the value of [tex]\((m \circ n)(-3)\)[/tex] is [tex]\(-3\)[/tex].
