The inverse of the function is f⁺ = -x² + 2x - 1)
The domain of the inverse function is set of all real numbers
How to find inverse of the function
The invers of the function is solved by solving for x in terms of y where
f(x) = y = √(-x) + 1
solving for x
y = √(-x) + 1
(y - 1)² = -x
x = -(y - 1)²
interchanging the variable
y = -(x - 1)²
expanding
y = -(x - 1) (x - 1)
y = -(x² - x - x + 1)
y = -(x² - 2x + 1)
y = -x² + 2x - 1)
hence f⁺¹ = -x² + 2x - 1)
The domain of the function is all real numbers