inverse function

Question

determine inverse function of f(x)=-2(x-3)^2+1

Answer 1

f(x) = y = 2(x-3)^2 +1

switch x and y and solve for the new y

x = 2(y-3)^2 + 1

(x-1)/2 = (y-3)^2

y - 3 = + or -sqr[(x-1)/2]

y = 3 + sqr[(x-1)/2] = an inverse relation, but not an inverse function

there is no inverse function, unless you ignore either the - or + square root.

It's then an inverse function of half of the original function.