To determine the value of [tex]\((h \circ h)(10)\)[/tex] where [tex]\( h(x) = 6 - x \)[/tex], we must first understand the composition of functions.
The composition [tex]\((h \circ h)(x)\)[/tex] means [tex]\(h(h(x))\)[/tex]. Here's a step-by-step solution:
1. We start by applying the function [tex]\(h(x)\)[/tex] to 10.
[tex]\[
h(10) = 6 - 10 = -4
\][/tex]
2. Next, we need to apply the function [tex]\(h(x)\)[/tex] to the result from the first step, 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]
The correct answer is [tex]\(10\)[/tex].
