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

The inverse of f(x)=-x^2+4x+1 is 2-sqrt(-x+5),sqrt(-x+5)+2

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

inverse

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

2 - - x + 5, - x + 5 + 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 + 5, - x + 5 + 2

ln (5 x)

f (x) = - 4 x - 1

4 - 7 x

f (x) = x + 6

f (x) = \frac{x ^{2} + 4 x + 3}{x + 1}

What is the inverse of f(x)=-x^2+4x+1 ?
The inverse of f(x)=-x^2+4x+1 is 2-sqrt(-x+5),sqrt(-x+5)+2