Question

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

Answer 1

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

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 $f^{-1}x$

$f^{-1}x=\sqrt{x} - 7$

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

Learn more here: brainly.com/question/12220962