Mathematics · Topology
Let the functions f: &mathbb{R}2 → &mathbb{R} and g: &mathbb{R}2 → &mathbb{R} be given by f(x1, x2) = x12 + x22 - 2x1x2 and g(x1, x2) = 2x12 + 2x22 - x1x2. Consider the following statements: S1: For every compact subset K of &mathbb{R}, f-1(K) is compact. S2: For every compact subset K of &mathbb{R}, g-1(K) is compact. Then, which one of the following is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Neither S1 nor S2 is TRUE
- 2Both S1 and S2 are TRUE
- 3S2 is TRUE and S1 is FALSE✓
- 4S1 is TRUE and S2 is FALSE
Correct answer
S2 is TRUE and S1 is FALSE
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