Set g(x) as y. Then you get y = 2x^3 + 3. Switch Y with X and you get x = 2y^3 + 3. Now you can put everything with x getting, y = cuberoot[(x-3)/2]
[tex]g(x)=2x^3+3\to y=2x^3+3[/tex]
replace x with y
[tex]2y^3+3=x\ \ \ |-3\\\\2y^3=x-3\ \ \ |:2\\\\y^3=\dfrac{x-3}{2}\to y=\sqrt[3]{\dfrac{x-3}{2}}[/tex]
Answer: [tex]g^{-1}(x)=\sqrt[3]{\dfrac{x-3}{2}}[/tex]
