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

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

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

inverse

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

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

Solution steps

y = 2^{x - 1} + 3

Replace

x

with

y

x = 2^{y - 1} + 3

Solve for

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

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

f (x) = 3 x + 21

\frac{7 x + 3}{x - 5}

f (x) = lo g_{10} (x - 4)

f (x) = \frac{x + 4}{3 x - 5}

f (x) = 7 x + 14

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