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

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

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

inverse

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

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

Solution steps

y = 2^{x - 1} + 1

Replace

x

with

y

x = 2^{y - 1} + 1

Solve for

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

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

f (x) = \frac{x ^{2} + 3 x - 4}{x - 1}

f (x) = \frac{x ^{2} + 9 x - 6}{x - 6}

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

y = 4 x + 7

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