Question

Use algebra to find the inverse of the given one-to-one function. Can someone show me how to solve this problem?
f(x) = (x^5 + 9)^3

Answer 1

just like if you were solving
\[(x^5+9)^3=12\] for x, solve
\[(y^5+9)^3=x\] for y

Answer 2

\[(y^5+9)^3=x\]
\[y^5+9=\sqrt[3]{x}\]
\[y^5=\sqrt[3]{x}-9\]
\[y=\sqrt[5]{\sqrt[3]{x}-9}\]

Answer 3

Thank you!