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 (A) 3 (B) 9 (C) 2 (D) 4

Tardigrade Admin · 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

Q. If $f (x)$ is a continuous function such that its value $\forall x \in R$ is a rational number and $f (1) + f (2) = 6$ , then the value of $f (3)$ is equal to

$3$

$9$

$2$

$4$

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

Q. 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

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

Q. If $f (x)$ is a continuous function such that its value $\forall x \in R$ is a rational number and $f (1) + f (2) = 6$ , then the value of $f (3)$ is equal to

$3$

$9$

$2$

$4$

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