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

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

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

inverse

f (x) = 2^{2 - x}

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

Solution steps

y = 2^{2 - x}

Replace

x

with

y

x = 2^{2 - y}

Solve for

y, x = 2^{2 - y}

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

f (x) = - (x + 1)^{2} + 7

f (x) = (x + 2)^{3} + 2

f (x) = 4 x + 2 + 6

f (x) = 5 x + 25

f (x) = \frac{8 x - 1}{2}

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