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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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