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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = x^{4} - 4

f (x) = x^{4} - 7

f (x) = \frac{( 3 x - 1 )}{2}

lo g_{3} (3 x + 4)

5 x + \frac{5}{x}

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