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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = - 3 x + 2

f (x) = 2 x^{2} - 7 x - 3

f (x) = \frac{7 x}{2 + x}

(4615.98, 1 0^{16}), (31382.6, 1 0^{17})

y - 1 = \frac{2}{3} (x + 9)

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