What is the inverse of f(x)=-x^2+6x-4 ?

The inverse of f(x)=-x^2+6x-4 is 3-sqrt(-x+5),sqrt(-x+5)+3

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inverse of f(x)=-x^2+6x-4

inverse

f (x) = - x^{2} + 6 x - 4

3 - - x + 5, - x + 5 + 3

Solution steps

y = - x^{2} + 6 x - 4

Replace

x

with

y

x = - y^{2} + 6 y - 4

Solve for

y, x = - y^{2} + 6 y - 4

3 - - x + 5, - x + 5 + 3

\frac{5 + 2 x}{1 + x}

\frac{3 x + 4}{6 x - 1}

f (x) = \frac{5 x ^{2}}{x ^{2} - 4}

f (x) = \frac{1}{x ^{2}} - \frac{1}{x}

(2, 8), (4, 5)

What is the inverse of f(x)=-x^2+6x-4 ?
The inverse of f(x)=-x^2+6x-4 is 3-sqrt(-x+5),sqrt(-x+5)+3