What is the inverse of f(x)=-2*3^{2x-1}+1/2 ?

The inverse of f(x)=-2*3^{2x-1}+1/2 is (ln(-(3(2x-1))/4))/(2ln(3))

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inverse of f(x)=-2*3^{2x-1}+1/2

inverse

f (x) = - 2 \cdot 3^{2 x - 1} + \frac{1}{2}

\frac{ln ( - \frac{3 ( 2 x - 1 )}{4} )}{2 ln ( 3 )}

Solution steps

y = - 2 \cdot 3^{2 x - 1} + \frac{1}{2}

Replace

x

with

y

x = - 2 \cdot 3^{2 y - 1} + \frac{1}{2}

Solve for

y, x = - 2 \cdot 3^{2 y - 1} + \frac{1}{2}

\frac{ln ( - \frac{3 ( 2 x - 1 )}{4} )}{2 ln ( 3 )}

y = \frac{1}{1 - b ^{x}}

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

\frac{2}{s + 1}

f (x) = 3 - \frac{1}{x - 4}

f (x) = \frac{x + 2 π}{8 π} - 2

What is the inverse of f(x)=-2*3^{2x-1}+1/2 ?
The inverse of f(x)=-2*3^{2x-1}+1/2 is (ln(-(3(2x-1))/4))/(2ln(3))