What is the inverse of f(x)=-x^2+6x-1 ?

The inverse of f(x)=-x^2+6x-1 is 3-sqrt(-x+8),sqrt(-x+8)+3

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inverse of f(x)=-x^2+6x-1

inverse

f (x) = - x^{2} + 6 x - 1

3 - - x + 8, - x + 8 + 3

Solution steps

y = - x^{2} + 6 x - 1

Replace

x

with

y

x = - y^{2} + 6 y - 1

Solve for

y, x = - y^{2} + 6 y - 1

3 - - x + 8, - x + 8 + 3

x = 3^{y}

f (x) = 2 + lo g_{2} (1 - x)

y = - 3 x + 12

g (x) = \frac{3 x + 4}{2 x - 5}

69 - 15 x

What is the inverse of f(x)=-x^2+6x-1 ?
The inverse of f(x)=-x^2+6x-1 is 3-sqrt(-x+8),sqrt(-x+8)+3