Question:
Consider the following two statements.
P : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that f is continuous at x = 1 and g is discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Q : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that both f and g are discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Which one of the following holds ?
Consider the following two statements.
P : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that f is continuous at x = 1 and g is discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Q : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that both f and g are discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Which one of the following holds ?
P : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that f is continuous at x = 1 and g is discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Q : There exist functions f: ℝ → ℝ, g: ℝ → ℝ such that both f and g are discontinuous at x = 1 but g ∘ f is continuous at x = 1.
Which one of the following holds ?
Updated On: Oct 1, 2024
- Both P and Q are true
- Both P and Q are false
- P is true but Q is false
- P is false but Q is true
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The Correct Option is A
Solution and Explanation
The correct option is (A) : Both P and Q are true.
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