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

The inverse of f(x)=sqrt(x/(2x-1)) is (x^2)/(2x^2-1)

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inverse of f(x)=sqrt(x/(2x-1))

inverse

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

\frac{x ^{2}}{2 x ^{2} - 1}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x ^{2}}{2 x ^{2} - 1}

\frac{5 x + 4}{7 x - 5}

\frac{x}{x ^{2} - 3}

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

\frac{2 x ^{2} - 22 x + 48}{2 x ^{2} - 25 x + 72}

(x - 8)^{3}

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