Question

If f(x) = x³, then f¯ ¹(x) =

Answer 1

From

`\begin{gathered} f(x)=x^3 \\ to\text{ get f}^(-1)(x),\text{ we put y = f\lparen x\rparen,} \end{gathered}`

we have

`\begin{gathered} y=f(x)=x^3 \\ y=x^3 \\ then\text{ make x the subject} \end{gathered}`

take the cube root of both sides

`\begin{gathered} \sqrt[3]{y}=\sqrt[3]{x^3} \\ \sqrt[3]{y}=x \end{gathered}`

now replace y with x and x with f inverse,

we have answer as

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