What is the inverse of f(x)=(x+2)/(x^2+2) ?

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

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inverse of f(x)=(x+2)/(x^2+2)

inverse

f (x) = \frac{x + 2}{x ^{2} + 2}

\frac{1 + 1 - 4 x ( 2 x - 2 )}{2 x}, \frac{1 - 1 - 4 x ( 2 x - 2 )}{2 x}

Solution steps

y = \frac{x + 2}{x ^{2} + 2}

Replace

x

with

y

x = \frac{y + 2}{y ^{2} + 2}

Solve for

y, x = \frac{y + 2}{y ^{2} + 2}

\frac{1 + 1 - 4 x ( 2 x - 2 )}{2 x}, \frac{1 - 1 - 4 x ( 2 x - 2 )}{2 x}

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

\frac{1}{7} (x + 5)^{3}

4 x^{2} + 12 x + 15

f (x) = 3 + 5 - x

f (x) = \frac{5 x + 4}{2}

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