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

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

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

inverse

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

\frac{ln ( 2 x )}{ln ( 2 )}, - \frac{ln ( 2 x )}{ln ( 2 )}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{ln ( 2 x )}{ln ( 2 )}, - \frac{ln ( 2 x )}{ln ( 2 )}

54.7928711

\frac{( 5 x + 2 )}{x - 3}

12 + 2 x - 2

\frac{7}{t ^{\frac{4}{3}}}

f (x) = \frac{2 x}{3}

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