Question

What is the inverse of this equation
F(x)=-(x-2)^2 +9

Answer 1

F^-1(x) = 2 + sqrt(-(x - 9))

Explanation:

To find the inverse of F(x) = -(x - 2)^2 + 9, we can follow these steps:

Replace F(x) with y: y = -(x - 2)^2 + 9

Solve for x in terms of y:

y - 9 = -(x - 2)^2

sqrt(-(y - 9)) = x - 2

x = 2 + sqrt(-(y - 9))

Replace x with F^-1(x) to get the inverse function:

F^-1(x) = 2 + sqrt(-(x - 9))

Therefore, the inverse of F(x) = -(x - 2)^2 + 9 is F^-1(x) = 2 + sqrt(-(x - 9)).