What is the inverse of f(x)=2^{x-3}+1 ?

The inverse of f(x)=2^{x-3}+1 is (ln(x-1))/(ln(2))+3

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inverse of f(x)=2^{x-3}+1

inverse

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

\frac{ln ( x - 1 )}{ln ( 2 )} + 3

Solution steps

y = 2^{x - 3} + 1

Replace

x

with

y

x = 2^{y - 3} + 1

Solve for

y, x = 2^{y - 3} + 1

\frac{ln ( x - 1 )}{ln ( 2 )} + 3

f (x) = 1.2 (3)^{x - 1} + 2

f (x) = 9 x - 1

x^{3} + 3

y = 2 x + 3

\frac{4 x + 9}{3 x - 6}

What is the inverse of f(x)=2^{x-3}+1 ?
The inverse of f(x)=2^{x-3}+1 is (ln(x-1))/(ln(2))+3