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

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

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

inverse

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

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

Solution steps

y = 2^{3 - x} - 2

Replace

x

with

y

x = 2^{3 - y} - 2

Solve for

y, x = 2^{3 - y} - 2

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

\frac{1}{2} 2 x - 8 - 7

f (x) = 4 - x + 1

x^{\frac{23}{11}} - x^{\frac{12}{11}}

\frac{1}{x ^{2} + 7}

\frac{x + 1}{x - 1}

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