Let f:[0,1] \rightarrow \mathbb{R} and g:[0,1] \rightarrow \mathbb{R} be defined as follows : f(x) \table= 1 \text{ if } x \text{ is rational } ; =0 \text{ if } x \text{ is irrational }] and g(x) \table =0 \text{ if } x \text{ is rational };=1 \text{ if } x \text{ is irrational }] then

Correct Answer is : f+g is continuous at the point x=23 but f and g are discontinuous at x=23.

f and g are continuous at the point x=\frac{1}{2}.

f+g is continuous at the point x=\frac{2}{3} but f and g are discontinuous at x=\frac{2}{3}.

f(x) \cdot g(x)>0 for some points x \in(0,1).

f+g is not differentiable at the point x=\frac{3}{4}.

WBJEE 2025 Math Paper

Question : 75 of 75

Marks: +1, -0

Let f:[0,1]⟶ℝ and g:[0,1]⟶ℝ be defined as follows :
f(x)‌

=1‌ if ‌x‌ is rational ‌

‌=0‌ if ‌x‌ is irrational ‌

] and
g(x)‌

=0‌ if ‌x‌ is rational

=1‌ if ‌x‌ is irrational

] then

Go to Question:

Prev Question