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Find the entire domain on which the function f is one-to-one and non-decreasing. Write the domain in interval notation.

Find The Entire Domain On Which The Function F Is Onetoone And Nondecreasing Write The Domain In Interval Notation class=

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Abidemiokinidn

The inverse of the function y =  (x+7)² is [tex]f^{-1}x=\sqrt{x} - 7[/tex]

From the given function f(x) = (x+7)²

Let y = f(x), the expression becomes:

y =  (x+7)²

Replace y with x

x = (y+7)²

Maker y the subject of the formula

x = (y+7)²

Take the square root of both sides

√x = √(y+7)²

√x  = y + 7

y = √x  - 7

Replace y with [tex]f^{-1}x[/tex]

[tex]f^{-1}x=\sqrt{x} - 7[/tex]

Hence the inverse of the function y =  (x+7)² is [tex]f^{-1}x=\sqrt{x} - 7[/tex]

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