To determine which expression is equivalent to [tex]\((s t)(6)\)[/tex], let's analyze the given options:
1. [tex]\(s(t(6))\)[/tex]:
This expression implies that you first apply the function [tex]\(t\)[/tex] to 6, and then apply the function [tex]\(s\)[/tex] to the result of [tex]\(t(6)\)[/tex].
2. [tex]\(s(x) \cdot t(6)\)[/tex]:
This expression implies that you multiply the result of the function [tex]\(s\)[/tex] applied to [tex]\(x\)[/tex] (which is not necessarily 6) with the result of the function [tex]\(t\)[/tex] applied to 6.
3. [tex]\(s(6) \cdot t(6)\)[/tex]:
This expression implies that you first apply the function [tex]\(s\)[/tex] to 6, and then apply the function [tex]\(t\)[/tex] to 6, and then multiply the two results together.
4. [tex]\(6 \cdot s(x) \cdot t(x)\)[/tex]:
This expression implies that you multiply 6 by the result of the function [tex]\(s\)[/tex] applied to some [tex]\(x\)[/tex], and then multiply by the result of the function [tex]\(t\)[/tex] applied to the same [tex]\(x\)[/tex].
Given the correct result is [tex]\(3\)[/tex], we need to match this to the correct option. The interpretation for [tex]\((s t)(6)\)[/tex] that matches getting a result of [tex]\(3\)[/tex] is indeed represented by the expression [tex]\(s(6) \cdot t(6)\)[/tex].
This indicates that you should apply each function ([tex]\(s\)[/tex] and [tex]\(t\)[/tex]) separately to 6, and then multiply the results together.
So, the expression equivalent to [tex]\((s t)(6)\)[/tex] is:
[tex]\[ s(6) \cdot t(6) \][/tex]
