What is the inverse of f(x)=-9(1/9)^x+1 ?

The inverse of f(x)=-9(1/9)^x+1 is -(ln(-(x-1)/9))/(2ln(3))

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inverse of f(x)=-9(1/9)^x+1

inverse

f (x) = - 9 (\frac{1}{9})^{x} + 1

- \frac{ln ( - \frac{x - 1}{9} )}{2 ln ( 3 )}

Solution steps

y = - 9 (\frac{1}{9})^{x} + 1

Replace

x

with

y

x = - 9 (\frac{1}{9})^{y} + 1

Solve for

y, x = - 9 (\frac{1}{9})^{y} + 1

- \frac{ln ( - \frac{x - 1}{9} )}{2 ln ( 3 )}

What is the inverse of f(x)=-9(1/9)^x+1 ?
The inverse of f(x)=-9(1/9)^x+1 is -(ln(-(x-1)/9))/(2ln(3))