Answer to Question #88310 in Algebra for Shivam Nishad

Question

Which of the following statements are true? Give reasons for your answers.
i) sin^-1(x²/y) is a homogeneous function of x and y

Answer 1

$False\\ Function\; f(x)\; is\; homogeneous\; if f(kx)=kf(x)\; for\; all\; real\;k.\\ f(kx)=asin(\frac{k^2x^2}{ky})=asin(\frac{kx^2}{y})\;is \; not\; equal \;to\;kf(x) \; for \;all\;k.$