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

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

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inverse of f(x)=(2x+1)/(2x-4)

inverse

f (x) = \frac{2 x + 1}{2 x - 4}

\frac{1 + 4 x}{2 ( - 1 + x )}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{1 + 4 x}{2 ( - 1 + x )}

f (x) = \frac{8}{x + 4}

x^{3} + 1

2^{- x} - 4

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

f (x) = 2 x + 4

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