Question

PPLICATIONS
The function y= A(r)= r ^2 a one-to-one function that uses a circle's radius as an input and gives the
circle's area as its output. Selected values of this function are shown in the table below.

Answer 1

All relations that have an inverse are functions.

• The value of  $A^{-1}(9\pi)$ is 3
• The value of  $A^{-1}(36\pi)$ is 6

The function is given as:

$\mathbf{A(r) =\pi r^2}$

(a) The value of $A^{-1}(9\pi)$

From the table (see attachment), we have:

$A(3) = 9\pi$

Take inverse of both sides

$3 = A^{-1}(9\pi)$

Rewrite as:

$A^{-1}(9\pi) = 3$

Hence, the value of  $A^{-1}(9\pi)$ is 3

(b) The value of $A^{-1}(36\pi)$

From the table (see attachment), we have:

$A(6) = 36\pi$

Take inverse of both sides

$6 = A^{-1}(36\pi)$

Rewrite as:

$A^{-1}(36\pi) = 6$

Hence, the value of  $A^{-1}(36\pi)$ is 6

Read more about inverse functions at:

https://brainly.com/question/10300045