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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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