MyloveG560020 MyloveG560020
  • 25-10-2022
  • Mathematics
contestada

Find the inverse of the function on the given domain. f(x)=(x−5)^2, [5,∞)

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KayleannaT412457 KayleannaT412457
  • 25-10-2022

To answer this question, first, we set the following equation:

[tex]y=(x-5)^2,[/tex]

and solve it for x.

Taking the square root, we get:

[tex]\sqrt[]{y}=x-5.[/tex]

Adding 5 to both sides of the equation, we get:

[tex]\sqrt[]{y}+5=x.[/tex]

Now, we exchange x for y:

[tex]y=\sqrt[]{x}+5.[/tex]

Therefore:

[tex]f^{-1}(x)=\sqrt[]{x}+5.[/tex]

Answer:

[tex]f^{-1}(x)=\sqrt[]{x}+5.[/tex]

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