What is the inverse of f(x)=(2x^2-1)/(3x) ?

The inverse of f(x)=(2x^2-1)/(3x) is (3x+sqrt(9x^2+8))/4 ,(3x-sqrt(9x^2+8))/4

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inverse of f(x)=(2x^2-1)/(3x)

inverse

f (x) = \frac{2 x ^{2} - 1}{3 x}

\frac{3 x + 9 x ^{2} + 8}{4}, \frac{3 x - 9 x ^{2} + 8}{4}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 x + 9 x ^{2} + 8}{4}, \frac{3 x - 9 x ^{2} + 8}{4}

What is the inverse of f(x)=(2x^2-1)/(3x) ?
The inverse of f(x)=(2x^2-1)/(3x) is (3x+sqrt(9x^2+8))/4 ,(3x-sqrt(9x^2+8))/4