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

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

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inverse of f(x)=-x^2+4x-3

inverse

f (x) = - x^{2} + 4 x - 3

2 - - x + 1, - x + 1 + 2

Solution steps

y = - x^{2} + 4 x - 3

Replace

x

with

y

x = - y^{2} + 4 y - 3

Solve for

y, x = - y^{2} + 4 y - 3

2 - - x + 1, - x + 1 + 2

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

16 x^{2} - 72 x + 88

f (x) = - \frac{3}{8} x - \frac{3}{2}

f (x) = (ln (x)) - 1

f (x) = - 9 - x^{2}

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