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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

f (x) = - 2 (x + 3)^{2} - 4

f (x) = \frac{6 x - 5}{x + 3}

y = \frac{3}{4} x + 2 - 1

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

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