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

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

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

inverse

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

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

Solution steps

y = 2^{x - 1} + 2

Replace

x

with

y

x = 2^{y - 1} + 2

Solve for

y, x = 2^{y - 1} + 2

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

y = \frac{x}{2} + 3

y = - \frac{2}{3} x + 1

100 - x

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

3 tan^{3} (x)

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