Question 1199941
Switch to x,y description.
{{{y=-x^2+8x-14}}}
Now to find the inverse, interchange x and y and solve for y. 
This new y is the inverse of the original function.
{{{x=-y^2+8x-14}}}
{{{y^2-8x+14=-x}}}
Complete the square,
{{{y^2-8x+16+14=-x+16}}}
{{{(y-4)^2+14=-x+16}}}
{{{(y-4)^2=2-x}}}
{{{y-4= 0 +- sqrt(2-x)}}}
The zero is the first term on the right hand side to make the plus/minus sign work correctly,
{{{y=4 +- sqrt(2-x)}}}
Since the term under the radical must be non-negative,
{{{2-x>=0}}}
{{{x<=2}}}