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

The inverse of f(x)=2x^2+x is (-1+sqrt(1+8x))/4 ,(-1-sqrt(1+8x))/4

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

inverse

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

\frac{- 1 + 1 + 8 x}{4}, \frac{- 1 - 1 + 8 x}{4}

Solution steps

y = 2 x^{2} + x

Replace

x

with

y

x = 2 y^{2} + y

Solve for

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

\frac{- 1 + 1 + 8 x}{4}, \frac{- 1 - 1 + 8 x}{4}

\frac{6}{1 + x ^{2}}

\frac{1 + x}{1 - x}

x^{2} - 5 x - 6

f (x) = \frac{7}{2 - x}

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

What is the inverse of f(x)=2x^2+x ?
The inverse of f(x)=2x^2+x is (-1+sqrt(1+8x))/4 ,(-1-sqrt(1+8x))/4