What is the inverse of f(x)=(sqrt(x))/(x-3) ?

The inverse of f(x)=(sqrt(x))/(x-3) is (6x^2+1+sqrt(12x^2+1))/(2x^2),(6x^2+1-sqrt(12x^2+1))/(2x^2)

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inverse of f(x)=(sqrt(x))/(x-3)

inverse

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

\frac{6 x ^{2} + 1 + 12 x ^{2} + 1}{2 x ^{2}}, \frac{6 x ^{2} + 1 - 12 x ^{2} + 1}{2 x ^{2}}

Solution steps

y = \frac{x}{x - 3}

Replace

x

with

y

x = \frac{y}{y - 3}

Solve for

y, x = \frac{y}{y - 3}

\frac{6 x ^{2} + 1 + 12 x ^{2} + 1}{2 x ^{2}}, \frac{6 x ^{2} + 1 - 12 x ^{2} + 1}{2 x ^{2}}

What is the inverse of f(x)=(sqrt(x))/(x-3) ?
The inverse of f(x)=(sqrt(x))/(x-3) is (6x^2+1+sqrt(12x^2+1))/(2x^2),(6x^2+1-sqrt(12x^2+1))/(2x^2)