What is the inverse of f(x)=5^{x^2},x<= 0 ?

The inverse of f(x)=5^{x^2},x<= 0 is sqrt((ln(x))/(ln(5))),-sqrt((ln(x))/(ln(5)))

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inverse of f(x)=5^{x^2},x<= 0

inverse

f (x) = 5^{x^{2}}, x \leq 0

\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 )}

What is the inverse of f(x)=5^{x^2},x<= 0 ?
The inverse of f(x)=5^{x^2},x<= 0 is sqrt((ln(x))/(ln(5))),-sqrt((ln(x))/(ln(5)))