What is the inverse of f(x)= 1/(\frac{2x-1){3-x}} ?

The inverse of f(x)= 1/(\frac{2x-1){3-x}} is (3+x)/(2x+1)

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inverse of f(x)= 1/(\frac{2x-1){3-x}}

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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