If f x is a continuous function such that its value ∀ x ∈ R is a rational number and f 1 + f 2 = 6 , then the value of f 3 is equal to

Question

If f x is a continuous function such that its value ∀ x ∈ R is a rational number and f 1 + f 2 = 6 , then the value of f 3 is equal to, 3, 9, 2, 4

MARKS App · Accepted Answer

Since f x is continuous and attains only rational values, then by intermediate value theorem, f x is a constant function. i.e. f 1 = f 2 = 3