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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.

Sagot :

MrRoyal

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

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