If f(x)= -4x^2+7 and x≤0, what is the equation of the inverse function?

Question

The answer is supposed to be f^-1(x)= -[√(7-x)]/2, but this is what I did:

x=-4y^2+7
-4y^2=x-7
y^2=(x-7)/-4
y= √[(x-7)/-4]

Did I do something wrong?

By the way, for the original function, the domain would be x≤0, but would the range be (-∞,7]?

Thanks!