IITM BS Question 8 - Week 9 Practice

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IITM BS Question 8 - Week 9 Practice | Prasnya

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Q8Comprehension7 Marks21 Dec 2025

Passage

Based on the above data, answer the given subquestions. Consider the function

f: \mathbb{R}^2 \to \mathbb{R}

defined by

f(x, y) = e^{x+y}

, for all

(x, y) \in \mathbb{R}^2

For any function

g: \mathbb{R}^2 \to \mathbb{R}

, the level set of

g

c \in \mathbb{R}

, denoted by

L_c(g)

, is defined as the set of points in

\mathbb{R}^2

that are mapped to

c

, i.e.,

L_c(g) = \{(x, y) \in \mathbb{R}^2 \mid g(x, y) = c\}

. Choose all the correct statements from the following.

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21 Dec 2025

Mathematics 2 · Week 9

Q8.For any function

g: \mathbb{R}^2 \to \mathbb{R}

, the level set of

g

c \in \mathbb{R}

, denoted by

L_c(g)

, is defined as the set of points in

\mathbb{R}^2

that are mapped to

c

, i.e.,

L_c(g) = \{(x, y) \in \mathbb{R}^2 \mid g(x, y) = c\}

. Choose all the correct statements from the following.@passage

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