To determine the value of [tex]\((h \circ h)(10)\)[/tex], let's proceed step by step.
First, we need to understand the composition of the function [tex]\(h\)[/tex]. The composition [tex]\((h \circ h)(x)\)[/tex] means we apply the function [tex]\(h\)[/tex] twice. In other words:
[tex]\[
(h \circ h)(x) = h(h(x))
\][/tex]
Given the function [tex]\(h(x)\)[/tex]:
[tex]\[
h(x) = 6 - x
\][/tex]
1. First Application of [tex]\(h\)[/tex]:
We apply [tex]\(h\)[/tex] to [tex]\(10\)[/tex]:
[tex]\[
h(10) = 6 - 10 = -4
\][/tex]
2. Second Application of [tex]\(h\)[/tex]:
Now, we need to apply [tex]\(h\)[/tex] again to the result we obtained, which is [tex]\(-4\)[/tex]:
[tex]\[
h(-4) = 6 - (-4) = 6 + 4 = 10
\][/tex]
Therefore, the value of [tex]\((h \circ h)(10)\)[/tex] is [tex]\(10\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{10}
\][/tex]
