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

The inverse of f(x)=(1+2^x)/(4-2^x) is (ln(-\frac{1-4x)/(1+x))}{ln(2)}

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

(- \frac{7}{3}, \frac{1}{3}), (- \frac{5}{3}, - \frac{7}{3})

5 + x

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

(- 1, - 9), (6, 8)

What is the inverse of f(x)=(1+2^x)/(4-2^x) ?
The inverse of f(x)=(1+2^x)/(4-2^x) is (ln(-\frac{1-4x)/(1+x))}{ln(2)}