COMEDK · Maths · 24. Functions
Which of the following is not a homogenous function of \(x\) and \(y\)
- A \(\cos ^2\left(\dfrac{y}{x}\right)+\dfrac{y}{x}\)
- B \(2 x-y\)
- C \(\sin x-\cos y\)
- D \(x^2+2 x y\)
Answer & Solution
Correct Answer
(C) \(\sin x-\cos y\)
Step-by-step Solution
Detailed explanation
A function \(f(x, y)\) is homogeneous of degree \(n\) if \(f(tx, ty) = t^n f(x, y)\) for any non-zero constant \(t\). For option (1), \(f(tx, ty) = \cos^2(\dfrac{ty}{tx}) + \dfrac{ty}{tx} = \cos^2(\dfrac{y}{x}) + \dfrac{y}{x} = t^0 f(x, y)\), which is homogeneous of degree 0.…
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