SOLUTION: Find the inverse function of f(x)=-x^2+8x-14 and x ≤4. Find the domain of this inverse function.

Algebra ->  Rational-functions -> SOLUTION: Find the inverse function of f(x)=-x^2+8x-14 and x ≤4. Find the domain of this inverse function.       Log On


   

Question 1199941: Find the inverse function of f(x)=-x^2+8x-14 and x ≤4. Find the domain of this inverse function.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Switch to x,y description.
y=-x%5E2%2B8x-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%5E2%2B8x-14
y%5E2-8x%2B14=-x
Complete the square,
y%5E2-8x%2B16%2B14=-x%2B16
%28y-4%29%5E2%2B14=-x%2B16
%28y-4%29%5E2=2-x
y-4=+0+%2B-+sqrt%282-x%29
The zero is the first term on the right hand side to make the plus/minus sign work correctly,
y=4+%2B-+sqrt%282-x%29
Since the term under the radical must be non-negative,
2-x%3E=0
x%3C=2