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

f (x) = \frac{2 ^{x} + 8}{3 - 2 ^{x}}

\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 )}

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

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

f (x) = \frac{ln ( x - 5 )}{2}

\frac{x - 3}{2 x + 1}

f (x) = 6 + ln (x)

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)}