What is the inverse of f(x)=(sqrt(x+3))/(x-2) ?

The inverse of f(x)=(sqrt(x+3))/(x-2) is (4x^2+1+sqrt(20x^2+1))/(2x^2),(4x^2+1-sqrt(20x^2+1))/(2x^2)

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inverse of f(x)=(sqrt(x+3))/(x-2)

inverse

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

\frac{4 x ^{2} + 1 + 20 x ^{2} + 1}{2 x ^{2}}, \frac{4 x ^{2} + 1 - 20 x ^{2} + 1}{2 x ^{2}}

Solution steps

y = \frac{x + 3}{x - 2}

Replace

x

with

y

x = \frac{y + 3}{y - 2}

Solve for

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

\frac{4 x ^{2} + 1 + 20 x ^{2} + 1}{2 x ^{2}}, \frac{4 x ^{2} + 1 - 20 x ^{2} + 1}{2 x ^{2}}

What is the inverse of f(x)=(sqrt(x+3))/(x-2) ?
The inverse of f(x)=(sqrt(x+3))/(x-2) is (4x^2+1+sqrt(20x^2+1))/(2x^2),(4x^2+1-sqrt(20x^2+1))/(2x^2)