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

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

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

inverse

\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) = 4 x^{2} + 1, x \geq 0

- x^{2} - 4 x + 4

f (x) = 10 x^{3} + 3

\frac{2 x}{x - 1}

f (x) = 6.5 - 12 x

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