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

The inverse of f(x)=(sqrt(x+1))/(x-2) is (4x^2+1+sqrt(12x^2+1))/(2x^2),(4x^2+1-sqrt(12x^2+1))/(2x^2)

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

inverse

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

\frac{4 x ^{2} + 1 + 12 x ^{2} + 1}{2 x ^{2}}, \frac{4 x ^{2} + 1 - 12 x ^{2} + 1}{2 x ^{2}}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{4 x ^{2} + 1 + 12 x ^{2} + 1}{2 x ^{2}}, \frac{4 x ^{2} + 1 - 12 x ^{2} + 1}{2 x ^{2}}

5 x^{2} - \frac{6}{7}

g (x) = x^{2} + 2

f (x) = 3 x^{2} + 2 y^{2} - 6 x - 12 y + 15 = 0

g (x) = x^{2} - 6

(X + 2)^{2} - (X - 2)^{2} + 24 X

What is the inverse of f(x)=(sqrt(x+1))/(x-2) ?
The inverse of f(x)=(sqrt(x+1))/(x-2) is (4x^2+1+sqrt(12x^2+1))/(2x^2),(4x^2+1-sqrt(12x^2+1))/(2x^2)