What is the inverse of f(x)=(2x+3)/(1+4x) ?

The inverse of f(x)=(2x+3)/(1+4x) is (3-x)/(2(-1+2x))

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inverse of f(x)=(2x+3)/(1+4x)

inverse

f (x) = \frac{2 x + 3}{1 + 4 x}

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

Solution steps

y = \frac{2 x + 3}{1 + 4 x}

Replace

x

with

y

x = \frac{2 y + 3}{1 + 4 y}

Solve for

y, x = \frac{2 y + 3}{1 + 4 y}

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

f (x) = 2 + ln (2 x - 1)

f (x) = \frac{3 x + 7}{x - 6}

f (x) = 2 (3 x + 1) + 4

x^{5} - 4

\frac{3 t + 2}{t + 1}

What is the inverse of f(x)=(2x+3)/(1+4x) ?
The inverse of f(x)=(2x+3)/(1+4x) is (3-x)/(2(-1+2x))