What is the inverse of f(x)=2^{-(x+13)}+1 ?

The inverse of f(x)=2^{-(x+13)}+1 is -(ln(x-1))/(ln(2))-13

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inverse of f(x)=2^{-(x+13)}+1

inverse

f (x) = 2^{- (x + 13)} + 1

- \frac{ln ( x - 1 )}{ln ( 2 )} - 13

Solution steps

y = 2^{- (x + 13)} + 1

Replace

x

with

y

x = 2^{- (y + 13)} + 1

Solve for

y, x = 2^{- (y + 13)} + 1

- \frac{ln ( x - 1 )}{ln ( 2 )} - 13

f (x) = \frac{2 x - 3}{3 - x}

f (x) = - 3 x + 2

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

f (x) = \frac{7 x}{2 + x}

(4615.98, 1 0^{16}), (31382.6, 1 0^{17})

What is the inverse of f(x)=2^{-(x+13)}+1 ?
The inverse of f(x)=2^{-(x+13)}+1 is -(ln(x-1))/(ln(2))-13