What is the inverse of f(x)=sqrt(-(x-2)^2)-3 ?

The inverse of f(x)=sqrt(-(x-2)^2)-3 is 2-sqrt(-x^2-6x-9),sqrt(-x^2-6x-9)+2

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inverse of f(x)=sqrt(-(x-2)^2)-3

inverse

f (x) = - (x - 2)^{2} - 3

2 - - x^{2} - 6 x - 9, - x^{2} - 6 x - 9 + 2

Solution steps

y = - (x - 2)^{2} - 3

Replace

x

with

y

x = - (y - 2)^{2} - 3

Solve for

y, x = - (y - 2)^{2} - 3

2 - - x^{2} - 6 x - 9, - x^{2} - 6 x - 9 + 2

What is the inverse of f(x)=sqrt(-(x-2)^2)-3 ?
The inverse of f(x)=sqrt(-(x-2)^2)-3 is 2-sqrt(-x^2-6x-9),sqrt(-x^2-6x-9)+2