What is the inverse of (2^x+1)/(5-2^x) ?

The inverse of (2^x+1)/(5-2^x) is (ln(-\frac{1-5x)/(1+x))}{ln(2)}

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inverse of (2^x+1)/(5-2^x)

inverse

\frac{2 ^{x} + 1}{5 - 2 ^{x}}

\frac{ln ( - \frac{1 - 5 x}{1 + x} )}{ln ( 2 )}

Solution steps

y = \frac{2 ^{x} + 1}{5 - 2 ^{x}}

Replace

x

with

y

x = \frac{2 ^{y} + 1}{5 - 2 ^{y}}

Solve for

y, x = \frac{2 ^{y} + 1}{5 - 2 ^{y}}

\frac{ln ( - \frac{1 - 5 x}{1 + x} )}{ln ( 2 )}

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

f (x) = 3 - x + 4

\frac{4 x ^{2} + 7}{4}

f (x) = 5 5 x + 4

x - 1 - 3

What is the inverse of (2^x+1)/(5-2^x) ?
The inverse of (2^x+1)/(5-2^x) is (ln(-\frac{1-5x)/(1+x))}{ln(2)}