What is the inverse of f(x)=4-(1/2)^{x-2} ?

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

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inverse of f(x)=4-(1/2)^{x-2}

inverse

f (x) = 4 - (\frac{1}{2})^{x - 2}

- \frac{ln ( 4 - x )}{ln ( 2 )} + 2

Solution steps

y = 4 - (\frac{1}{2})^{x - 2}

Replace

x

with

y

x = 4 - (\frac{1}{2})^{y - 2}

Solve for

y, x = 4 - (\frac{1}{2})^{y - 2}

- \frac{ln ( 4 - x )}{ln ( 2 )} + 2

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