What is the inverse of f(x)=x^2+5x+1 ?

The inverse of f(x)=x^2+5x+1 is (-5+sqrt(4x+21))/2 ,(-5-sqrt(4x+21))/2

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inverse of f(x)=x^2+5x+1

inverse

f (x) = x^{2} + 5 x + 1

\frac{- 5 + 4 x + 21}{2}, \frac{- 5 - 4 x + 21}{2}

Solution steps

y = x^{2} + 5 x + 1

Replace

x

with

y

x = y^{2} + 5 y + 1

Solve for

y, x = y^{2} + 5 y + 1

\frac{- 5 + 4 x + 21}{2}, \frac{- 5 - 4 x + 21}{2}

- 5 + 5 (x - 3)^{2}

y = 5 x - 7

y = 5 x - 8

f (x) = 2 sin (4 x)

\frac{x ^{2}}{x - 5} \cdot \frac{5 x - 10}{2 x}

What is the inverse of f(x)=x^2+5x+1 ?
The inverse of f(x)=x^2+5x+1 is (-5+sqrt(4x+21))/2 ,(-5-sqrt(4x+21))/2