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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (5) = x - 4

y = (x - 1)^{2} + 1

- x^{2} + 10

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

y = (x - 1)^{2} + 3

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