Answer:
It is proved that [tex]f(x)g(x)=|x|=|x-4|-4[/tex].
Step-by-step explanation:
Given functions are,
[tex]f(x)=|x|[/tex]
[tex]g9x)=|x-4|-4[/tex]
To show,
[tex]f(x)g(x)=|x|=|x-4|-4[/tex]
Consider,
[tex](fg)(x)=f(g(x))=f(|x-4|-4)=||x-4|-4|[/tex]
now if,
[tex]x>4\implies x-4>0[/tex] then [tex](fg)(x)=||x-4|-4|=|x-4|-4[/tex]
[tex]x<4\implies x-4<0[/tex] then [tex](fg)(x)=||x-4|-4|=||-(x+4)|-4|=|x+4-4|=|x|[/tex]
Hence the reslt.
