What is the inverse of f(x)=(2^x+8)/(3-2^x) ?

The inverse of f(x)=(2^x+8)/(3-2^x) is (ln(-\frac{8-3x)/(1+x))}{ln(2)}

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inverse of f(x)=(2^x+8)/(3-2^x)

inverse

\frac{ln ( - \frac{8 - 3 x}{1 + x} )}{ln ( 2 )}

Solution steps

y = \frac{2 ^{x} + 8}{3 - 2 ^{x}}

Replace

x

with

y

x = \frac{2 ^{y} + 8}{3 - 2 ^{y}}

Solve for

y, x = \frac{2 ^{y} + 8}{3 - 2 ^{y}}

\frac{ln ( - \frac{8 - 3 x}{1 + x} )}{ln ( 2 )}

What is the inverse of f(x)=(2^x+8)/(3-2^x) ?
The inverse of f(x)=(2^x+8)/(3-2^x) is (ln(-\frac{8-3x)/(1+x))}{ln(2)}