Question

Show step by step:

Find the inverse for y=(x-3)³+1

Answer 1

$y=(x-3)^3+1$

Interchange the variables:

$x=(y-3)^3+1$

Solve for $y$ :

$x=(y-3)^3+1$

$-(y-3)^3=-x+1$

$(y-3)^3=x-1$

$y-3=\sqrt[3]{x-1}$

$y=\sqrt[3]{x-1}+3$

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

$f^{-1}(x)=\sqrt[3]{x-1}+3$