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

The inverse of f(x)=1-2/(sqrt(x+3)) is 4/(x^2-2x+1)-3

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inverse of f(x)=1-2/(sqrt(x+3))

inverse

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

\frac{4}{x ^{2} - 2 x + 1} - 3

Solution steps

y = 1 - \frac{2}{x + 3}

Replace

x

with

y

x = 1 - \frac{2}{y + 3}

Solve for

y, x = 1 - \frac{2}{y + 3}

\frac{4}{x ^{2} - 2 x + 1} - 3

5 (x + 3)

\frac{x}{3 x + 6}

\frac{x}{x - 2}

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

x^{2} - 3 x

What is the inverse of f(x)=1-2/(sqrt(x+3)) ?
The inverse of f(x)=1-2/(sqrt(x+3)) is 4/(x^2-2x+1)-3