What is the inverse of f(x)=-x^2+4x-1 ?

The inverse of f(x)=-x^2+4x-1 is 2-sqrt(-x+3),sqrt(-x+3)+2

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inverse of f(x)=-x^2+4x-1

inverse

f (x) = - x^{2} + 4 x - 1

2 - - x + 3, - x + 3 + 2

Solution steps

y = - x^{2} + 4 x - 1

Replace

x

with

y

x = - y^{2} + 4 y - 1

Solve for

y, x = - y^{2} + 4 y - 1

2 - - x + 3, - x + 3 + 2

f (x) = \frac{x + 3}{x - 2}

\frac{2}{3} x + \frac{1}{2}

f (x) = \frac{x - 4}{7}

- 1 - x + 3

f (x) = \frac{1}{2} x + \frac{9}{2}

What is the inverse of f(x)=-x^2+4x-1 ?
The inverse of f(x)=-x^2+4x-1 is 2-sqrt(-x+3),sqrt(-x+3)+2