Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Analysis Continuity & Differentiability
Let f : ℝ → ℝ be defined as follows
\(f(x)=\left\{\begin{array}{c} 1, \text { if } x=0 \\ 0, \text { if } x ∈ \mathbb{R} \backslash \mathbb{Q} \\ 3, \text { if } x=\frac{m}{n} \end{array}\right.\)
Then
1
f is continuous only at the irrational.
2
f is continuous everywhere except 0
3
f is no-where continuous.
4
f is continuous everywhere
5
Question Not Attempted