Question

Let f(x) = (x – 10)^9– 5, determine f^-1(x)

Answer 1

- We are asked to find the inverse of the function below:

`f(x)=(x-10)^9-5`

- The solution steps for finding the inverse is given below:

`\begin{gathered} Let\text{ }f(x)=y \\ \\ y=(x-10)^9-5 \\ \\ \text{ Add 5 to both sides} \\ y+5=(x-10)^9 \\ \\ Take\text{ the 9th root of both sides} \\ \sqrt[9]{y+5}=x-10 \\ \\ \text{ Add 10 to both sides} \\ x=\sqrt[9]{y+5}+10 \\ \\ \text{ Thus, if we make x = y and y = x, we have that} \\ \\ y=\sqrt[9]{x+5}+10 \\ \\ Let\text{ }y=f^(-1)(x) \\ \\ \therefore f^(-1)(x)=\sqrt[9]{x+5}+10 \end{gathered}`

Final Answer

The inverse of function f(x) is:

`f^(-1)(x)=\sqrt[9]{x+5}+10`