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: To get the function g, shift f DOWN by 4 units and to the RIGHT by 4 units.

Explanation:

Khan

Answer 2

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

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<4\implies x-4<0` then
`(fg)(x)=||x-4|-4|=||-(x+4)|-4|=|x+4-4|=|x|`

Hence the reslt.