[tex]h(x)=(f\circ g)(x)\\\\h(x)=\sqrt[3]{x+3};\ f(x)=\sqrt[3]{x+2}\\\\h(x)=\sqrt[3]{x+1+2}=\sqrt[3]{(x+1)+2}=\sqrt[3]{g(x)+2}\to \boxed{g(x)=x+1}[/tex]
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[tex]f(x)=2x;\ g(x)=2x-1;\ h(x)=\sqrt{x}\\\\(f\circ g\circ h)(9)=?\\\\h(9)=\sqrt9=3\\\\(g\circ h)(9)=g(3)=2(3)-1=6-1=5\\\\(f\circ g\circ h)(9)=f(5)=2(5)=10\\------------------------------\\other\ method:\\\\(f\circ g\circ h)(x)=2(2\sqrt{x}-1)=4\sqrt{x}-2\\\\(f\circ g\circ h)(9)=4\sqrt9-2=4(3)-2=12-2=10[/tex]
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[tex]f(x)=4x+1;\ g(x)=x^2-5\\\\(f\circ g)(4)=?\\\\g(4)=4^2-5=16-5=11\\(f\circ g)(4)=f(11)=4(11)+1=44+1=45\\----------------------------------\\other\ method:\\\\(f\circ g)(x)=4(x^2-5)+1=4x^2-20+1=4x^2-19\\\\(f\circ g)(4)=4(4)^2-19=4(16)-19=64-19=45[/tex]
