What is the inverse of f(x)=(2x+3)/(5x+4) ?

The inverse of f(x)=(2x+3)/(5x+4) is (3-4x)/(5x-2)

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inverse of f(x)=(2x+3)/(5x+4)

inverse

f (x) = \frac{2 x + 3}{5 x + 4}

\frac{3 - 4 x}{5 x - 2}

Solution steps

y = \frac{2 x + 3}{5 x + 4}

Replace

x

with

y

x = \frac{2 y + 3}{5 y + 4}

Solve for

y, x = \frac{2 y + 3}{5 y + 4}

\frac{3 - 4 x}{5 x - 2}

\frac{7}{x + 3}

y = \frac{4 x ^{2}}{x ^{2} - 2 x - 3}

x^{3} - 12 x + 3

4 x^{7} + 6

\frac{9 - x ^{2}}{2 x ^{2}}

What is the inverse of f(x)=(2x+3)/(5x+4) ?
The inverse of f(x)=(2x+3)/(5x+4) is (3-4x)/(5x-2)