Answer :
To solve for [tex]\( (h \circ h)(10) \)[/tex] where [tex]\( h(x) = 6 - x \)[/tex], we need to apply the function [tex]\( h \)[/tex] twice. Let's go through the steps to find the value of [tex]\( (h \circ h)(10) \)[/tex] step-by-step.
### Step 1: Calculate [tex]\( h(10) \)[/tex]
We start by evaluating the function [tex]\( h \)[/tex] at [tex]\( x = 10 \)[/tex].
[tex]\[ h(10) = 6 - 10 \][/tex]
[tex]\[ h(10) = -4 \][/tex]
### Step 2: Apply [tex]\( h \)[/tex] again to the result of Step 1
Now, we need to apply the function [tex]\( h \)[/tex] to the value obtained in Step 1, which is [tex]\( -4 \)[/tex].
[tex]\[ h(-4) = 6 - (-4) \][/tex]
[tex]\[ h(-4) = 6 + 4 \][/tex]
[tex]\[ h(-4) = 10 \][/tex]
Thus, the value of [tex]\( (h \circ h)(10) \)[/tex] is [tex]\( 10 \)[/tex].
### Conclusion
The correct choice is:
[tex]\[ \boxed{10} \][/tex]
### Step 1: Calculate [tex]\( h(10) \)[/tex]
We start by evaluating the function [tex]\( h \)[/tex] at [tex]\( x = 10 \)[/tex].
[tex]\[ h(10) = 6 - 10 \][/tex]
[tex]\[ h(10) = -4 \][/tex]
### Step 2: Apply [tex]\( h \)[/tex] again to the result of Step 1
Now, we need to apply the function [tex]\( h \)[/tex] to the value obtained in Step 1, which is [tex]\( -4 \)[/tex].
[tex]\[ h(-4) = 6 - (-4) \][/tex]
[tex]\[ h(-4) = 6 + 4 \][/tex]
[tex]\[ h(-4) = 10 \][/tex]
Thus, the value of [tex]\( (h \circ h)(10) \)[/tex] is [tex]\( 10 \)[/tex].
### Conclusion
The correct choice is:
[tex]\[ \boxed{10} \][/tex]
