Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Continuity & Differentiability
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?
1
Both P and Q are true
2
Both P and Q are false
3
P is true but Q is false
4
P is false but Q is true