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

The inverse of f(x)=((2x-1))/(x+2) is (-1-2x)/(x-2)

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

f (x) = (x + 1)^{2} - 1

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

f (x) = 3 (\frac{2}{x}) - 10

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

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