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

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

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

inverse

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

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

Solution steps

y = 1 + 2^{x - 1}

Replace

x

with

y

x = 1 + 2^{y - 1}

Solve for

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

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

f (x) = 3960 (1.06)^{x}

f (x) = (2 x)^{\frac{4}{5}}

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

f (x) = \frac{1}{π} arctan (x - 3) + 0.5 π

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