What is the inverse of f(x)=2^{3-x} ?

The inverse of f(x)=2^{3-x} is -(ln(x)-3ln(2))/(ln(2))

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inverse of f(x)=2^{3-x}

inverse

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

- \frac{ln ( x ) - 3 ln ( 2 )}{ln ( 2 )}

Solution steps

y = 2^{3 - x}

Replace

x

with

y

x = 2^{3 - y}

Solve for

y, x = 2^{3 - y}

- \frac{ln ( x ) - 3 ln ( 2 )}{ln ( 2 )}

y = - 3 (x + 5)^{2} - 4

f (x) = 8 x - 4 x^{2}

- x^{2} + 4 x - 3

\frac{9 x}{3 - x}

2^{3 - x} - 7

What is the inverse of f(x)=2^{3-x} ?
The inverse of f(x)=2^{3-x} is -(ln(x)-3ln(2))/(ln(2))