Functions

S=(0,1)∪(1,2)∪(3,4)‌ and ‌T={0,1,2,3}
Let domain and co-domain of a function y=f(x) are S and T respectively.
(A) There are infinitely many elements in domain and four elements in co-domain.
⇒ There are infinitely many functions from S to T.
⇒ Option (A) is correct
(B) If number of elements in domain is greater than number of elements in co-domain, then number of strictly increasing function is zero.
⇒ Option (B) is incorrect
(C) Maximum number of continuous functions =4×4×4=64
(Every subset (0,1),(1,2),(3,4) has four choices)
∵‌‌64<120⇒ option (C) is correct.
(D) For every point at which f(x) is continuous, f(x)=0
⇒‌‌ Every continuous function from S to T is differentiable.