What is the inverse of sqrt((4-x^2)/(x+4)) ?

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

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inverse of sqrt((4-x^2)/(x+4))

inverse

\frac{4 - x ^{2}}{x + 4}

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

Solution steps

y = \frac{4 - x ^{2}}{x + 4}

Replace

x

with

y

x = \frac{4 - y ^{2}}{y + 4}

Solve for

y, x = \frac{4 - y ^{2}}{y + 4}

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

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