State true or false:
$F (x, y) = e^{y / x} + ln x - ln y$ is homogeneous function of degree zero.

True

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False

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Solution

The correct option is A True
$F (x, y) = e^{y / x} + ln x - ln y \Rightarrow F (t x, t y) = e^{t y / t x} + ln t x - ln t y = e^{y / x} + ln x + ln t - ln t - ln y = e^{y / x} + ln x - ln y = t^{0} F (x, y)$
Hence, degree is $0$ .

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