What is the inverse of f(x)=3^{2x-1}-2 ?

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

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inverse of f(x)=3^{2x-1}-2

inverse

f (x) = 3^{2 x - 1} - 2

\frac{ln ( 3 ( x + 2 ) )}{2 ln ( 3 )}

Solution steps

y = 3^{2 x - 1} - 2

Replace

x

with

y

x = 3^{2 y - 1} - 2

Solve for

y, x = 3^{2 y - 1} - 2

\frac{ln ( 3 ( x + 2 ) )}{2 ln ( 3 )}

\frac{3 s + 5}{s ^{2} + 4 s + 13}

\frac{2 s + 1}{s ^{2} - 2 s - 2}

ln (4 - 2 x)

f (x) = f (x) = 49 - x^{2}

f (x) = f (x) = 6 x - 5

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