What is the inverse of f(x)=(3-2x)/(2x-5) ?

The inverse of f(x)=(3-2x)/(2x-5) is (3+5x)/(2(1+x))

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inverse of f(x)=(3-2x)/(2x-5)

inverse

f (x) = \frac{3 - 2 x}{2 x - 5}

\frac{3 + 5 x}{2 ( 1 + x )}

Solution steps

y = \frac{3 - 2 x}{2 x - 5}

Replace

x

with

y

x = \frac{3 - 2 y}{2 y - 5}

Solve for

y, x = \frac{3 - 2 y}{2 y - 5}

\frac{3 + 5 x}{2 ( 1 + x )}

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

f (x) = \frac{3 - 2 x}{x - 5}

f (x) = \frac{5 - 3 x}{2 x - 3}

f (x) = \frac{5 - 2 x}{4 x - 2}

f (x) = 2 (x - 3)^{2} + 5

What is the inverse of f(x)=(3-2x)/(2x-5) ?
The inverse of f(x)=(3-2x)/(2x-5) is (3+5x)/(2(1+x))