What is the inverse of f(x)=sqrt(x/(3x+5)) ?

The inverse of f(x)=sqrt(x/(3x+5)) is -(5x^2)/(3x^2-1)

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inverse of f(x)=sqrt(x/(3x+5))

inverse

f (x) = \frac{x}{3 x + 5}

- \frac{5 x ^{2}}{3 x ^{2} - 1}

Solution steps

y = \frac{x}{3 x + 5}

Replace

x

with

y

x = \frac{y}{3 y + 5}

Solve for

y, x = \frac{y}{3 y + 5}

- \frac{5 x ^{2}}{3 x ^{2} - 1}

What is the inverse of f(x)=sqrt(x/(3x+5)) ?
The inverse of f(x)=sqrt(x/(3x+5)) is -(5x^2)/(3x^2-1)