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

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

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

inverse

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

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

Solution steps

y = \frac{1}{2} (1 - \frac{1}{2})^{x - 1}

Replace

x

with

y

x = \frac{1}{2} (1 - \frac{1}{2})^{y - 1}

Solve for

y, x = \frac{1}{2} (1 - \frac{1}{2})^{y - 1}

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

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