Hey, I am asked to find the inverse of [MATH]y = x\sqrt{2+x^2} [/MATH] if such exist.
x = [MATH]y\sqrt{2+y^2} [/MATH][MATH]y = \frac{x}{\sqrt{2+x^2}}[/MATH] , I know that if x is positive, so is y because [MATH]\sqrt{2+x^2}[/MATH] is always [MATH]\geq[/MATH] 0 no matter x, and it is multiplied by x so the sign in front of y is dependent on the sign in front of x. But how do I go on from here?
x = [MATH]y\sqrt{2+y^2} [/MATH][MATH]y = \frac{x}{\sqrt{2+x^2}}[/MATH] , I know that if x is positive, so is y because [MATH]\sqrt{2+x^2}[/MATH] is always [MATH]\geq[/MATH] 0 no matter x, and it is multiplied by x so the sign in front of y is dependent on the sign in front of x. But how do I go on from here?