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\begin{aligned} f(x)&=|x| \\\\ g(x)&=|x - 4| - 4 \end{aligned} f(x) g(x) ​ =∣x∣ =∣x−4∣−4 ​ We can think of ggg as a translated (shifted) version of fff.

Respuesta :

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.

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