Answer :
Solution
- We are asked to find the inverse of the function below:
[tex]f(x)=(x-10)^9-5[/tex]- The solution steps for finding the inverse is given below:
[tex]\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}[/tex]Final Answer
The inverse of function f(x) is:
[tex]f^{-1}(x)=\sqrt[9]{x+5}+10[/tex]