what's the inverse of f(x)=-(x-2)^1/2+4

Write y, instead of f(x), then for an inverse, exchange x and y,

So we get: x = -(y – 2 )^1/2 + 4

x - 4 = -(y – 2 )^1/2

multiply by – 1:

4 – x = (y – 2 )^1/2

Square both sides:

(4 – x)^2 = y – 2

FOIL: 16 – 8x + x^2 = y – 2

SO: y = x^2 – 8x + 16 or y = (x – 4)^2

So we get: x = -(y – 2 )^1/2 + 4

x - 4 = -(y – 2 )^1/2

multiply by – 1:

4 – x = (y – 2 )^1/2

Square both sides:

(4 – x)^2 = y – 2

FOIL: 16 – 8x + x^2 = y – 2

SO: y = x^2 – 8x + 16 or y = (x – 4)^2