What is the inverse of f(x)=4^{x-1}+1 ?

The inverse of f(x)=4^{x-1}+1 is (ln(x-1))/(2ln(2))+1

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inverse of f(x)=4^{x-1}+1

inverse

f (x) = 4^{x - 1} + 1

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

Solution steps

y = 4^{x - 1} + 1

Replace

x

with

y

x = 4^{y - 1} + 1

Solve for

y, x = 4^{y - 1} + 1

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

f (x) = 5 x^{4} - 5

f (x) = e^{5 x + 3} + 5

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

g (x) = \frac{x}{10} + 2

f (x) = \frac{100 y - 1}{y}

What is the inverse of f(x)=4^{x-1}+1 ?
The inverse of f(x)=4^{x-1}+1 is (ln(x-1))/(2ln(2))+1