Given:
There are given that the function:
[tex]f(x)=(x-19)^2[/tex]
Explanation:
According to the question:
We need to find the inverse of the function.
Then,
To find the inverse, first exchange f(x) into y:
So,
[tex]\begin{gathered} f(x)=(x-19)^{2} \\ y=(x-19)^2...(1) \end{gathered}[/tex]
Then,
We need to exchange x into y:
So,
[tex]\begin{gathered} y=(x-19)^2 \\ x=(y-19)^2...(2) \end{gathered}[/tex]
Then,
We need findthe value for y:
[tex]\begin{gathered} \begin{equation*} x=(y-19)^2 \end{equation*} \\ \pm\sqrt{x}=y-19 \\ y=\pm\sqrt{x}+19 \\ y=\sqrt{x}+19,-\sqrt{x}+19 \end{gathered}[/tex]
Then,
[tex]f^{-1}(x)=\sqrt{x}+19,-\sqrt{x}+19[/tex]
Final answer:
Hence, the inverse of the given function is show below:
[tex]f^{-1}(x)=\sqrt{x}+19[/tex]
