Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 41

$(f\circ g\circ h) (x)=\sqrt{x^{6}+4x^{3}+1}$

$(f\circ g\circ h) (x)=f[g(h(x))]$ $g(h(x))=[h(x)]^{2}=(x^{3}+2)^{2}$ $f[g(h(x))]=f[(x^{3}+2)^{2}]=\sqrt{(x^{3}+2)^{2}-3}$ $=\sqrt{(x^{6}+4x^{3}+4)-3}$ $=\sqrt{x^{6}+4x^{3}+1}$