Certainly! Let's work through the problem step by step.
The function given is [tex]\( h(x) = 6 - x \)[/tex].
1. First, apply the function [tex]\( h \)[/tex] to the number 10. This is denoted as [tex]\( h(10) \)[/tex]:
[tex]\[
h(10) = 6 - 10 = -4
\][/tex]
2. Next, we need to find [tex]\( (h \circ h)(10) \)[/tex], which means we need to apply the function [tex]\( h \)[/tex] to the result of [tex]\( h(10) \)[/tex]. In other words, we need to find [tex]\( h(h(10)) \)[/tex]:
- We already found that [tex]\( h(10) = -4 \)[/tex], so now we need to find [tex]\( h(-4) \)[/tex]:
[tex]\[
h(-4) = 6 - (-4) = 6 + 4 = 10
\][/tex]
So the value of [tex]\( (h \circ h)(10) \)[/tex] is [tex]\( 10 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{10} \][/tex]
