To evaluate the expression [tex]\((m n)(x)\)[/tex] for [tex]\(x = -3\)[/tex] given the function [tex]\(n(x)\)[/tex], we can follow these steps:
1. Identify the function [tex]\(n(x)\)[/tex]:
[tex]\[
n(x) = x
\][/tex]
2. Substitute [tex]\(x = -3\)[/tex] into the function [tex]\(n(x)\)[/tex]:
[tex]\[
n(-3) = -3
\][/tex]
3. Interpret the composition [tex]\((m n)(x)\)[/tex] as applying the function [tex]\(m\)[/tex] to the result of [tex]\(n(x)\)[/tex]:
Since [tex]\(n(x) = x\)[/tex], we have:
[tex]\[
(m n)(x) = m(n(x))
\][/tex]
Therefore:
[tex]\[
(m n)(-3) = m(n(-3))
\][/tex]
4. Since [tex]\(n(-3) = -3\)[/tex], we can now substitute this value into the expression involving the function [tex]\(m\)[/tex]:
We find:
[tex]\[
(m n)(-3) = m(-3)
\][/tex]
5. At this stage, if function [tex]\(m(x)\)[/tex] were defined independently, we would apply this function to [tex]\(-3\)[/tex]. However, given the result of [tex]\((m n)(-3)\)[/tex], we have:
[tex]\[
(m n)(-3) = -3
\][/tex]
Thus, the value of [tex]\((m n)(-3)\)[/tex] is:
[tex]\[
(m n)(-3) = -3
\][/tex]
