What is the inverse of f(x)=sqrt((3x)/(4-x)) ?

The inverse of f(x)=sqrt((3x)/(4-x)) is (4x^2)/(x^2+3)

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inverse of f(x)=sqrt((3x)/(4-x))

inverse

f (x) = \frac{3 x}{4 - x}

\frac{4 x ^{2}}{x ^{2} + 3}

Solution steps

y = \frac{3 x}{4 - x}

Replace

x

with

y

x = \frac{3 y}{4 - y}

Solve for

y, x = \frac{3 y}{4 - y}

\frac{4 x ^{2}}{x ^{2} + 3}

\frac{7}{( x - 4 ) ^{2}}

f (x) = \frac{1}{3} (x - 2)^{2} + 8

2 ln (\frac{x + 3}{5})

y = x - 8

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

What is the inverse of f(x)=sqrt((3x)/(4-x)) ?
The inverse of f(x)=sqrt((3x)/(4-x)) is (4x^2)/(x^2+3)