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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

x^{2} - 6 x + 8

6 sin (x)

y = - 1 x

sin^{2} (x) - 2 cos (x)

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

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