What is the inverse of (-4x^2+2x)/(3x^2-1) ?

The inverse of (-4x^2+2x)/(3x^2-1) is (1+sqrt(x(3x+4)+1))/(3x+4),(1-sqrt(x(3x+4)+1))/(3x+4)

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inverse of (-4x^2+2x)/(3x^2-1)

inverse

\frac{- 4 x ^{2} + 2 x}{3 x ^{2} - 1}

\frac{1 + x ( 3 x + 4 ) + 1}{3 x + 4}, \frac{1 - x ( 3 x + 4 ) + 1}{3 x + 4}

Solution steps

y = \frac{- 4 x ^{2} + 2 x}{3 x ^{2} - 1}

Replace

x

with

y

x = \frac{- 4 y ^{2} + 2 y}{3 y ^{2} - 1}

Solve for

y, x = \frac{- 4 y ^{2} + 2 y}{3 y ^{2} - 1}

\frac{1 + x ( 3 x + 4 ) + 1}{3 x + 4}, \frac{1 - x ( 3 x + 4 ) + 1}{3 x + 4}

f (x) = \frac{2 x ^{4} + 7}{x ^{2} + 1}

f (x) = f (x) = (x - 2)^{2} + 3

f (42) = 625 (1 - \frac{x}{50})^{2}

f (x) = \frac{2}{π} sin (r)

arctan (e^{2 x})

What is the inverse of (-4x^2+2x)/(3x^2-1) ?
The inverse of (-4x^2+2x)/(3x^2-1) is (1+sqrt(x(3x+4)+1))/(3x+4),(1-sqrt(x(3x+4)+1))/(3x+4)