Question

sin inverse( xsquare /y) is a homogeneous function of x and y.True or false?

Answer 1

Answer on Question #84273 – Math – Other

Question

sin inverse (xsquare /y) is a homogeneous function of x and y. True or false?

Solution

$$f(ax, ay) = \sin^{-1} \left(\frac{(ax)^2}{ay}\right) = \sin^{-1} \left(\frac{ax^2}{y}\right).$$

There is no such $k$ that $\sin^{-1}\left(\frac{ax^2}{y}\right) = a^k \sin^{-1}\left(\frac{x^2}{y}\right)$.

Function $\sin^{-1}\left(\frac{x^2}{y}\right)$ is not homogeneous.

**Answer:** False.

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