Question

let f and g be two functions from R into R,defines by f(x)=|x|+x and g(x)=|x|-x for all x€R find fog and gof

Answer 1

fog =2x -mod of x
gof =mod of x

Answer 2

Answer:

The value of fog is $f\circ g=||x|-x|+|x|-x$ and the value of gof is $g\circ f=||x|+x|-|x|-x$.

Step-by-step explanation:

The given functions are

$f(x)=|x|+x$

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

$f\circ g=f(g(x))$

$f\circ g=f(|x|-x)$

$f\circ g=||x|-x|+|x|-x$

$g\circ f=g(f(x))$

$g\circ f=g(|x|+x)$

$g\circ f=||x|+x|-|x|-x$

Therefore the value of fog is $f\circ g=||x|-x|+|x|-x$ and the value of gof is $g\circ f=||x|+x|-|x|-x$.