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

The inverse of f(x)=sqrt(x^2+x+2) is (-1+sqrt(4x^2-7))/2 ,(-1-sqrt(4x^2-7))/2

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inverse of f(x)=sqrt(x^2+x+2)

inverse

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

\frac{- 1 + 4 x ^{2} - 7}{2}, \frac{- 1 - 4 x ^{2} - 7}{2}

Solution steps

y = x^{2} + x + 2

Replace

x

with

y

x = y^{2} + y + 2

Solve for

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

\frac{- 1 + 4 x ^{2} - 7}{2}, \frac{- 1 - 4 x ^{2} - 7}{2}

What is the inverse of f(x)=sqrt(x^2+x+2) ?
The inverse of f(x)=sqrt(x^2+x+2) is (-1+sqrt(4x^2-7))/2 ,(-1-sqrt(4x^2-7))/2