Question

\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.

Answer 1

Answer:

It is proved that $f(x)g(x)=|x|=|x-4|-4$.

Step-by-step explanation:

Given functions are,

$f(x)=|x|$

$g9x)=|x-4|-4$

To show,

$f(x)g(x)=|x|=|x-4|-4$

Consider,

$(fg)(x)=f(g(x))=f(|x-4|-4)=||x-4|-4|$

now if,

$x>4\implies x-4>0$ then $(fg)(x)=||x-4|-4|=|x-4|-4$

$x$ then $(fg)(x)=||x-4|-4|=||-(x+4)|-4|=|x+4-4|=|x|$

Hence the reslt.