Question

Find the inverse of h(x)=2x^3+3​

Answer 1

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

`\stackrel{h(x)}{y}~~ = ~~2x^3+3\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^3 + 3} \\\\\\ x-3=2y^3\implies \cfrac{x-3}{2}=y^3\implies \sqrt[3]{\cfrac{x-3}{2}}=y=f^(-1)(x)`