What is the inverse of f(x)=sqrt((6+2x)/(6-2x)) ?

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

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inverse of f(x)=sqrt((6+2x)/(6-2x))

inverse

f (x) = \frac{6 + 2 x}{6 - 2 x}

- \frac{3 - 3 x ^{2}}{x ^{2} + 1}

Solution steps

y = \frac{6 + 2 x}{6 - 2 x}

Replace

x

with

y

x = \frac{6 + 2 y}{6 - 2 y}

Solve for

y, x = \frac{6 + 2 y}{6 - 2 y}

- \frac{3 - 3 x ^{2}}{x ^{2} + 1}

f (x) = \frac{x + 9}{1 - 2 x}

y = - x - 6

y = x^{2} + 6 x + 5

y = - x - 5

f (x) = 2 (x + 5)^{2} - 6

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