All relations that have an inverse are functions.
- The value of [tex]A^{-1}(9\pi)[/tex] is 3
- The value of [tex]A^{-1}(36\pi)[/tex] is 6
The function is given as:
[tex]\mathbf{A(r) =\pi r^2}[/tex]
(a) The value of [tex]A^{-1}(9\pi)[/tex]
From the table (see attachment), we have:
[tex]A(3) = 9\pi[/tex]
Take inverse of both sides
[tex]3 = A^{-1}(9\pi)[/tex]
Rewrite as:
[tex]A^{-1}(9\pi) = 3[/tex]
Hence, the value of [tex]A^{-1}(9\pi)[/tex] is 3
(b) The value of [tex]A^{-1}(36\pi)[/tex]
From the table (see attachment), we have:
[tex]A(6) = 36\pi[/tex]
Take inverse of both sides
[tex]6 = A^{-1}(36\pi)[/tex]
Rewrite as:
[tex]A^{-1}(36\pi) = 6[/tex]
Hence, the value of [tex]A^{-1}(36\pi)[/tex] is 6
Read more about inverse functions at:
https://brainly.com/question/10300045
