What is the inverse of f(x)=9*2^{2x-1}-1 ?

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

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inverse of f(x)=9*2^{2x-1}-1

inverse

f (x) = 9 \cdot 2^{2 x - 1} - 1

\frac{ln ( \frac{2 ( x + 1 )}{9} )}{2 ln ( 2 )}

Solution steps

y = 9 \cdot 2^{2 x - 1} - 1

Replace

x

with

y

x = 9 \cdot 2^{2 y - 1} - 1

Solve for

y, x = 9 \cdot 2^{2 y - 1} - 1

\frac{ln ( \frac{2 ( x + 1 )}{9} )}{2 ln ( 2 )}

f (x) = 5 - \frac{1}{2} x

y = \frac{5 x - 3}{x}

f (x) = x^{2} + 4 x + 5, x \leq - 2

- 5 x - 6

f (x) = \frac{( 2 x + 5 )}{x - 11}

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