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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

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

2 x^{3} + 6 x^{2} + 3

f (x) = 2 - 9 x^{3}

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

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