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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = \frac{12 x}{8 x ^{2} + 1}

f (x) = x + 2 - 25 - 5 x

f (x) = 2 x^{2} - 1

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

f (x) = 99 \cdot (\frac{1}{2})^{x}

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