Which of the following is/are correct for the function $x cos \frac{y}{x}$ ?

Not homogenous

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Homogenous

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Degree =

1

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Degree=

2

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Solution

The correct options are
B Homogenous
C Degree = $1$
Let the given function be $f (x, y) = x cos (\frac{y}{x})$
Now, $f (k x, k y) = k x cos (\frac{k y}{k x})$
$f (k x, k y) = k x cos (\frac{k y}{k x}) = k x cos (\frac{y}{x}) = k f (x, y)$
$∴$ the function is homogeous as $k > 0$ and is of degree $1$ .

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