if ill get help ill appricate it im confused thanks precalulus hw

Question

Let

Find a domain on which  is one-to-one and non-decreasing

.Find the inverse of  restricted to this domain    

Answer 1

f(x) is a U shaped upward opening parabola with vertex & minimum point at (3,0)

the domain where f is non-decreasing is (3, infinity)

the inverse function is x= (y-3)^2 found by switching x and y and solving for y

y-3 = sqrx

y = sqrx + 3

f^-1(x) = sqrx + 3 with the same domain (3, infinity)

the inverse function is symmetric to f(x) about the line y=x-3, a 45 degree line through the vertex (3,0)

the inverse function is a rightward opening parabola, and just the top half of it, with the same vertex (3,0)