If $$f(x)=2x+$$|x|,$$g(x)=13(2x$$−|x|$$)$$ and $$h(x)=f(g(x))$$ then domain of $$sin$$−$$1$$⁡(h(h(h(h$$…$$h(x)…$$))))$$⏟n times is

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If $$f(x)=2x+$$|x|,$$g(x)=13(2x$$−|x|$$)$$ and $$h(x)=f(g(x))$$ then domain of $$sin$$−$$1$$⁡(h(h(h(h$$…$$h(x)…$$))))$$⏟n times  is

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fx $$=$$ $$2x+x$$, x≥$$0$$              $$=2x-x$$, x<$$0$$        then  $$fx=3x$$ ,x≥$$0$$         $$=x$$, x<$$0$$  $$gx=$$ $$132x-x$$, if x≥$$0$$         $$=132x+x$$,x<$$0$$               ⇒   $$gx=x3$$ , x≥$$0$$                $$=x$$,x<$$0$$ therefore $$fgx=3x3$$ $$=$$ x,  if x≥$$0$$                           $$=$$ x          , if x<$$0$$         ⇒  hx $$=x$$ , for all x∈R $$sin$$$$-1hhh$$......hx.....$$=$$$$sin$$$$-1x$$     , it's domain $$is=$$[$$-1$$,$$1$$]

$If f (x) = 2 x + | x |, g (x) = \frac{1}{3} (2 x - | x |) and h (x) = f (g (x)) then domain of \sin^{- 1} \underset{n times}{\underset{⏟}{(h (h (h (h \dots h (x) \dots))))}} is$

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If f(x)=2x+|x|,g(x)=13(2x−|x|) and h(x)=f(g(x)) then domain of sin−1⁡(h(h(h(h…h(x)…))))⏟n times is

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$If f (x) = 2 x + | x |, g (x) = \frac{1}{3} (2 x - | x |) and h (x) = f (g (x)) then domain of \sin^{- 1} \underset{n times}{\underset{⏟}{(h (h (h (h \dots h (x) \dots))))}} is$