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

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

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

inverse

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

\frac{2 + 5 x}{2 x - 3}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{2 + 5 x}{2 x - 3}

\frac{24 x}{x ^{2} + 16}

y = - lo g_{4} (x)

(\frac{2}{3})^{x}

f (x) = \frac{24 t}{t ^{2} + 16}

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