What is the inverse of f(x)=1-(0.9^x) ?

The inverse of f(x)=1-(0.9^x) is (ln(1-x))/(ln(0.9))

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inverse of f(x)=1-(0.9^x)

inverse

f (x) = 1 - (0. 9^{x})

\frac{ln ( 1 - x )}{ln ( 0.9 )}

Solution steps

y = 1 - 0. 9^{x}

Replace

x

with

y

x = 1 - 0. 9^{y}

Solve for

y, x = 1 - 0. 9^{y}

\frac{ln ( 1 - x )}{ln ( 0.9 )}

f (x) = 4 cos (x)

2 x + 7 + 5

y = \frac{5}{2} x + 4

\frac{( x - 3 )}{1 - 4 x}

f (x) = \frac{4 x + 6}{2 x - 3}

What is the inverse of f(x)=1-(0.9^x) ?
The inverse of f(x)=1-(0.9^x) is (ln(1-x))/(ln(0.9))