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

\frac{2}{3} e^{- \frac{2 x}{3}}

f (x) = 6 - \frac{5}{3} x

f (x) = x^{2} + 2 x - 3, x \leq - 2

f (x) = \frac{5 - 12 x}{6 + 10 x}

f (x) = \frac{x + 9}{x - 7}

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