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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = 3 x^{2} - 2 x + 1

f (x) = (x + 1)^{2} - 2, x \geq - 1

f (x) = 4 + x - 2

f (x) = x + 2 + 5

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

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