f(x)= |x| and g (x)= sin x

Range of f = (0, ∞) ⊂ Domain g (R) ⇒ gof exist

Range of g= [ – 1,1] ⊂ Domain f (R) ⇒ fog exist

Now, fog (x)= f(g(x)) = f(sin x) = |sin x| and

gof(x) = g(f(x)) = g(lxl) =sin |x|

Hence, fog(x) = |sin x| and gof(x) = sin |x|