Find the inverse of the function on the given domain

Question

Find the inverse of the function on the given domain

F(x) = (x-9)^2, the domainis [9, infinity)

Answer 1

y = (x-9)^2 is an upward opening parabola with vertex x=9, y=0 (9,0) = minimum point

switch x and y

x = (y-9)^2

solve for the new y. it's f^-1(x)

sqrx = y-9

y = 9+sqrx when x=9, y = 0 vertex is (0,9) where x =0 is the smallest x value of a rightward opening parabola. It's not an inverse function, not a function, if you use both - and + square roots of x

The + square root is the top half of a rightward opening parabola. That makes it a function and an inverse function.

the inverse is the mirror image or reflection of the original function reflected across the diagonal line, the 45 degree line with the x axis through the origin (0,0) every point on the original function has an inverse where x and y coordinates are switched. If (9,0) is on the original function, (0,9) is on the inverse function. IF (x,y) is a point on the original function, (y,x) is a point on the inverse function.