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If `f,g:R->R` be two functions defined as `f(x)=|x|+x` and `g(x)=|x|-x`. Find `fog` and `gof`. Hence find `fog(-3)`, `fog(5)` and `gof(-2)`.

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If `f,g:R->R` be two functions defined as `f(x)=|x|+x` and `g(x)=|x|-x`. Find `fog` and `gof`. Hence find `fog(-3)`, `fog(5)` and `gof(-2)`.
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`f(x)=|x|+x`
`g(x)=|x|-x`
`fog=f[g(x)]=|g(x)|g(x)`
`||x|-x|+|x|-x`
`gof=g[f(x)=|f(x)|-f(x)`
`||x|+x|=||x|+x|`
`fog(-3)=||-3|-(-3)|+|-3|-(-3)`
`=|3+3|+3+3=12`
`fog(5)=||5|-5|+|5|-5=0`
`gof(-2)=||-2|+2|-|2-2|=0-0=0`.
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