Question

F(x)=3(x^1/7 divided by 7 +4)
find f-¹(x).

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{f(x)}{y}~~ = ~~3\left(\cfrac{x^{(1)/(7)}}{7} + 4 \right)\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~3\left(\cfrac{y^{(1)/(7)}}{7} + 4 \right)} \\\\\\ \cfrac{x}{3}=\cfrac{y^{(1)/(7)}}{7} + 4\implies \cfrac{x}{3}-4=\cfrac{y^{(1)/(7)}}{7}\implies 7\left( \cfrac{x}{3}-4 \right)=y^{(1)/(7)} \\\\\\ 7\left( \cfrac{x}{3}-4 \right)=\sqrt[7]{y}\implies \left( ~~ 7\left( \cfrac{x}{3}-4 \right) ~~ \right)^7=\stackrel{f^(-1)(x)}{y}`