What is the inverse of f(x)=5^{x^2} ?

The inverse of f(x)=5^{x^2} is sqrt((ln(x))/(ln(5))),-sqrt((ln(x))/(ln(5)))

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inverse of f(x)=5^{x^2}

inverse

f (x) = 5^{x^{2}}

\frac{ln ( x )}{ln ( 5 )}, - \frac{ln ( x )}{ln ( 5 )}

Solution steps

y = 5^{x^{2}}

Replace

x

with

y

x = 5^{y^{2}}

Solve for

y, x = 5^{y^{2}}

\frac{ln ( x )}{ln ( 5 )}, - \frac{ln ( x )}{ln ( 5 )}

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

f (x) = \frac{x ^{4}}{7} + 27

f (x) = \frac{( - 8 x + 7 )}{( - 4 x + 3 )}

14 + 3 x

What is the inverse of f(x)=5^{x^2} ?
The inverse of f(x)=5^{x^2} is sqrt((ln(x))/(ln(5))),-sqrt((ln(x))/(ln(5)))