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

The inverse of f(x)=(sqrt(x))/(sqrt(x)-3) is (9x^2)/(x^2-2x+1)

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

inverse

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

\frac{9 x ^{2}}{x ^{2} - 2 x + 1}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{9 x ^{2}}{x ^{2} - 2 x + 1}

f (x) = \frac{1}{4} (x + 3)^{2} - 2

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

f (x) = 2 π r^{2} + 12 π r

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

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

What is the inverse of f(x)=(sqrt(x))/(sqrt(x)-3) ?
The inverse of f(x)=(sqrt(x))/(sqrt(x)-3) is (9x^2)/(x^2-2x+1)