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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

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

f (x) = 2 x + 3 - 4

y + 1

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