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

The inverse of f(x)=(3^x+1)/(2*3^x-1) is (ln(\frac{1+x)/(2x-1))}{ln(3)}

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

f (x) = \frac{( y ^{2} + 12 y + 36 )}{60}

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

sin (3 0^{\circ})

f (x) = 7 sin (x) - 2

What is the inverse of f(x)=(3^x+1)/(2*3^x-1) ?
The inverse of f(x)=(3^x+1)/(2*3^x-1) is (ln(\frac{1+x)/(2x-1))}{ln(3)}