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}

(4, \frac{3}{2}), (7, \frac{3}{5})

f (x) = tan (\frac{π}{2} x)

(7, - 1), (3, 8)

y + x = 5

f (x) = \frac{5}{x + 1}

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