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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

y = 3 ln (\frac{x + 5}{2})

f (x) = - 4 x + 7

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

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

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