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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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