Question

Find the inverse of h (x)=(x+4)^3-1

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}~~ = ~~(x+4)^3 - 1\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~(y+4)^3 -1} \\\\\\ x+1=(y+4)^3\implies \sqrt[3]{x+1}=y+4\implies \sqrt[3]{x+1}-4=y=h^(-1)(x)`