A function is homogeneous of degree if which relation is satisfied for all non-zero real scalars ?
Answer and explanation
Correct answer: C.
- Step 1: By definition, a function is homogeneous of degree if substituting and scales the output by .
- Step 2: Mathematically: .
Answer
.
Why not the others: Multiplying by is not the degree scaling law; placing inside arguments is invalid; and adding shifts defines translation invariance, not homogeneity.
Practise more Vectors, 3D Geometry and Probability.
Free questions with an explanation for every one, and full timed CBSE Class 12 mock tests.
More Vectors, 3D Geometry and Probability questions
- If are the direction cosines of a straight line in three-dimensional space, what is the value of ?
- Which formula gives the shortest distance between two skew lines and…
- If , , and , what is the value of ?
- Two events and with non-zero probabilities are statistically independent if and only if which equality holds?
- Bag I contains 3 red and 4 black balls, while Bag II contains 5 red and 6 black balls. One bag is chosen at random with equal probability an…
- A fair coin is tossed times. Let denote the number of heads obtained. What are the mean () and variance () of th…