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)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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 )}

f (x) = \frac{3 \cdot ( - 4 )}{2}

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

f (x) = - 35

5 x - 2 - 2

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

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)))