To find the value of [tex]\((h \circ h)(10)\)[/tex] where [tex]\(h(x) = 6 - x\)[/tex], we perform the following steps:
1. Evaluate [tex]\(h(10)\)[/tex]:
[tex]\[ h(10) = 6 - 10 \][/tex]
[tex]\[ h(10) = -4 \][/tex]
2. Evaluate [tex]\(h(h(10))\)[/tex]:
First, we need to recognize that [tex]\(h(h(10))\)[/tex] means we are applying the function [tex]\(h\)[/tex] to the result of [tex]\(h(10)\)[/tex], which we found to be [tex]\(-4\)[/tex].
[tex]\[ h(h(10)) = h(-4) \][/tex]
Now we evaluate [tex]\(h(-4)\)[/tex]:
[tex]\[ h(-4) = 6 - (-4) \][/tex]
[tex]\[ h(-4) = 6 + 4 \][/tex]
[tex]\[ h(-4) = 10 \][/tex]
Therefore, the value of [tex]\((h \circ h)(10)\)[/tex] is:
[tex]\[ \boxed{10} \][/tex]
