What is the inverse of f(x)=3^{x-1}-9 ?

The inverse of f(x)=3^{x-1}-9 is (ln(x+9))/(ln(3))+1

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inverse of f(x)=3^{x-1}-9

inverse

f (x) = 3^{x - 1} - 9

\frac{ln ( x + 9 )}{ln ( 3 )} + 1

Solution steps

y = 3^{x - 1} - 9

Replace

x

with

y

x = 3^{y - 1} - 9

Solve for

y, x = 3^{y - 1} - 9

\frac{ln ( x + 9 )}{ln ( 3 )} + 1

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

201

\frac{10}{13}

f (x) = (x + 3)^{2} - 5

f (x) = \frac{( 5 + x )}{6 - 2 x}

What is the inverse of f(x)=3^{x-1}-9 ?
The inverse of f(x)=3^{x-1}-9 is (ln(x+9))/(ln(3))+1