What is the inverse of f(x)=(x^2+5x)^{1/2} ?

The inverse of f(x)=(x^2+5x)^{1/2} is (-5+(25+4x^2)^{1/2})/2 ,(-5-(25+4x^2)^{1/2})/2

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inverse of f(x)=(x^2+5x)^{1/2}

inverse

f (x) = (x^{2} + 5 x)^{\frac{1}{2}}

\frac{- 5 + ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}, \frac{- 5 - ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}

Solution steps

y = (x^{2} + 5 x)^{\frac{1}{2}}

Replace

x

with

y

x = (y^{2} + 5 y)^{\frac{1}{2}}

Solve for

y, x = (y^{2} + 5 y)^{\frac{1}{2}}

\frac{- 5 + ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}, \frac{- 5 - ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}

e^{x + 1}

f (x) = \frac{x ^{7}}{8} + 8

f (x) = x^{2} - 2 x + 4

f (x) = \frac{1}{10} x - \frac{7}{10}

f (x) = \frac{x + 5}{x - 4}

What is the inverse of f(x)=(x^2+5x)^{1/2} ?
The inverse of f(x)=(x^2+5x)^{1/2} is (-5+(25+4x^2)^{1/2})/2 ,(-5-(25+4x^2)^{1/2})/2