What is the inverse of f(x)=e^{sqrt(x+x^2)} ?

The inverse of f(x)=e^{sqrt(x+x^2)} is (-1+sqrt(1+4ln^2(x)))/2 ,(-1-sqrt(1+4ln^2(x)))/2

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inverse of f(x)=e^{sqrt(x+x^2)}

inverse

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

\frac{- 1 + 1 + 4 ln ^{2} ( x )}{2}, \frac{- 1 - 1 + 4 ln ^{2} ( x )}{2}

Solution steps

y = e^{x + x^{2}}

Replace

x

with

y

x = e^{y + y^{2}}

Solve for

y, x = e^{y + y^{2}}

\frac{- 1 + 1 + 4 ln ^{2} ( x )}{2}, \frac{- 1 - 1 + 4 ln ^{2} ( x )}{2}

f (x) = x^{2} + 8 x + 4

\frac{8}{x x ^{2} - 4}

f (x) = x + x + 7

- x + 5

2 x^{2} + x

What is the inverse of f(x)=e^{sqrt(x+x^2)} ?
The inverse of f(x)=e^{sqrt(x+x^2)} is (-1+sqrt(1+4ln^2(x)))/2 ,(-1-sqrt(1+4ln^2(x)))/2