Question

Find the inverse of the function. f(x) = the cube root of quantity x divided by eight. - 4

Answer 1

$\bf f(x)=y=\sqrt[3]{\cfrac{x}{8}}-4\impliedby \textit{first, let's switch the variables about} \\\\\\ \underline{x}=\sqrt[3]{\cfrac{\underline{y}}{8}}-4\implies x+4=\sqrt[3]{\cfrac{\underline{y}}{8}}\implies (x+4)^3=\cfrac{y}{8} \\\\\\ \boxed{8(x+4)^3=y}\impliedby f^{-1}(x)$

Answer 2

Answer:

$f^{-1}(x)=8(x+4)^{3}$

Step-by-step explanation:

we have

$f(x)=\sqrt[3]{\frac{x}{8}}-4$

Let

$y=f(x)$

$y=\sqrt[3]{\frac{x}{8}}-4$

Exchanges the variable x for y and y for x

$x=\sqrt[3]{\frac{y}{8}}-4$

Isolate the variable y

$x+4=\sqrt[3]{\frac{y}{8}}$

elevates to the cube both members

$(x+4)^{3}=\frac{y}{8} \\ \\y=8(x+4)^{3}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=8(x+4)^{3}$ ------> inverse function