What is the inverse of f(x)=(4*3^x)/(6+3^x) ?

The inverse of f(x)=(4*3^x)/(6+3^x) is (ln(-\frac{6x)/(x-4))}{ln(3)}

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inverse of f(x)=(4*3^x)/(6+3^x)

inverse

f (x) = \frac{4 \cdot 3 ^{x}}{6 + 3 ^{x}}

\frac{ln ( - \frac{6 x}{x - 4} )}{ln ( 3 )}

Solution steps

y = \frac{4 \cdot 3 ^{x}}{6 + 3 ^{x}}

Replace

x

with

y

x = \frac{4 \cdot 3 ^{y}}{6 + 3 ^{y}}

Solve for

y, x = \frac{4 \cdot 3 ^{y}}{6 + 3 ^{y}}

\frac{ln ( - \frac{6 x}{x - 4} )}{ln ( 3 )}

What is the inverse of f(x)=(4*3^x)/(6+3^x) ?
The inverse of f(x)=(4*3^x)/(6+3^x) is (ln(-\frac{6x)/(x-4))}{ln(3)}