Answer
g(x)=-$\sqrt {x-2}$+2
Work Step by Step
First, f(x) is shifted 2 units to the right so we must subtract 2 from x to get:
g(x)=$\sqrt {x-2}$
Then, f(x) is reflected across the x-axis so we must multiply the function by 1 to get:
g(x)=-$\sqrt {x-2}$
Finally, f(x) is shifted 2 units upward so we must add 2 to the function to get:
g(x)=-$\sqrt {x-2}$+2
