Does function f(x,y) = \(Sin^{-1} [\frac{(\sqrt x+\sqrt y)}{\sqrt{x+y}}]\)

does-function-f-x-y-sin-1-frac-sqrt-x-sqrt-y-sqrt-x-y

Does function f(x,y) = \(Sin^{-1} [\frac{(\sqrt x+\sqrt y)}{\sqrt{x+y}}]\) can be solved by euler’ s theorem.

A. True

B. False

I got this question in an interview.

My doubt is from Partial Differentiation topic in portion Partial Differentiation of Engineering Mathematics

Correct option is B. False

Easy explanation: No this function cannot be written in form of x^n f(^y⁄x) hence it does not satisfies euler’s theorem.