What is the inverse of f(x)=2^{3-x}-7 ?

The inverse of f(x)=2^{3-x}-7 is -(ln(x+7)-3ln(2))/(ln(2))

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inverse of f(x)=2^{3-x}-7

inverse

f (x) = 2^{3 - x} - 7

- \frac{ln ( x + 7 ) - 3 ln ( 2 )}{ln ( 2 )}

Solution steps

y = 2^{3 - x} - 7

Replace

x

with

y

x = 2^{3 - y} - 7

Solve for

y, x = 2^{3 - y} - 7

- \frac{ln ( x + 7 ) - 3 ln ( 2 )}{ln ( 2 )}

f (x) = \frac{\frac{x}{1 + x}}{1 + \frac{x}{1 + x}}

x^{2} - 2

f (x) = 3 + sin (\frac{2 π}{3} x)

f (x) = ln (2 - 5 x^{2})

f (x) = 5^{- x}

What is the inverse of f(x)=2^{3-x}-7 ?
The inverse of f(x)=2^{3-x}-7 is -(ln(x+7)-3ln(2))/(ln(2))