Answer to Question #172367 in Algebra for william

Question

Show step by step:

Find the inverse for y=4³sqaure root of x-2

Answer 1

Solution:

$y=4\sqrt[3]{x-2}$

Interchange the variables:

$x=4\sqrt[3]{y-2}$

Solve for $y$ :

$x=4\sqrt[3]{y-2}$

$x^3=4^3(y-2)$

$x^3=64(y-2)$

$y-2=\frac{x^3}{64}$

$y=\frac{x^3}{64}+2$

Replace the $y$ with $f^{-1}(x)$ to show the final answer:

$f^{-1}(x)=\frac{x^3}{64}+2$

Answer:

$f^{-1}(x)=\frac{x^3}{64}+2$