Answer: 16
Step-by-step explanation:
The given function : [tex]h(x) =6 -x[/tex]
Then, the composition function of [tex](h\cdot h)(x)=h(x)\times h(x)[/tex]
[tex]\\\\\Rightarrow\ (h\cdot h)(x)=(6-x)(6-x)=(6-x)^2[/tex]
Using identity [tex](a-b)^2=a^2-2ab+b^2[/tex], we have
[tex](6-x)^2=6^2-(2)(6)(x)+x^2\\\\\Rightarrow\ (h\cdot h)(x)=(6-x)^2=36-12x+x^2[/tex]
Now, [tex](h\cdot h)(10)=36-12(10)+(10)^2[/tex]
[tex]=36-120+100=16[/tex]
Hence, the value of [tex](h\cdot h)(10)=16[/tex]
