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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

(- 7, 1), (3, - 5)

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

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

x = - 1, - 2

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