What is the inverse of f(x)=(2x+1)/(-4x+5) ?

The inverse of f(x)=(2x+1)/(-4x+5) is -(1-5x)/(2(1+2x))

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inverse of f(x)=(2x+1)/(-4x+5)

inverse

f (x) = \frac{2 x + 1}{- 4 x + 5}

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

Solution steps

y = \frac{2 x + 1}{- 4 x + 5}

Replace

x

with

y

x = \frac{2 y + 1}{- 4 y + 5}

Solve for

y, x = \frac{2 y + 1}{- 4 y + 5}

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

f (x) = x - \frac{x ^{2}}{12} - 2

f (x) = (x + 1)^{2} + 5

\frac{s + 3}{( s + 1 ) ( s + 4 )}

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

\frac{2 s + 3}{s ^{2} + 9}

What is the inverse of f(x)=(2x+1)/(-4x+5) ?
The inverse of f(x)=(2x+1)/(-4x+5) is -(1-5x)/(2(1+2x))