What is the inverse of 3^{x^2-1} ?

The inverse of 3^{x^2-1} is sqrt((ln(3x))/(ln(3))),-sqrt((ln(3x))/(ln(3)))

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inverse of 3^{x^2-1}

inverse

3^{x^{2} - 1}

\frac{ln ( 3 x )}{ln ( 3 )}, - \frac{ln ( 3 x )}{ln ( 3 )}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{ln ( 3 x )}{ln ( 3 )}, - \frac{ln ( 3 x )}{ln ( 3 )}

\frac{( x + 1 )}{x - 1}

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

f (x) = 0.17 - \frac{1}{0.17}

f (x) = (3 x - 4)^{\frac{1}{3}}

tan (- \frac{1}{3})

What is the inverse of 3^{x^2-1} ?
The inverse of 3^{x^2-1} is sqrt((ln(3x))/(ln(3))),-sqrt((ln(3x))/(ln(3)))