Let the function f(x) and g(x) be defined as f(x)=⎧⎨⎩√x0≤x<12−x1≤x<2f(x+2) ∀x∈R and g(x)=4f(3x)+1, ∀x∈R. Let A denotes the sum of all the solutions of the equation f(x)=0.6, 3≤x≤7. B denotes the fundamental period of g(x). C denotes the value of g′(6.75). Then, the value of [ABC] is (where [.] represents greatest integer function)

Let the function f(x) and g(x) be defined as f(x)=⎧⎨⎩√x0≤x

1.	Let the function f(x) and g(x) be defined as f(x)=⎧⎨⎩√x0≤x<12−x1≤x<2f(x+2) ∀x∈R and g(x)=4f(3x)+1, ∀x∈R. Let A denotes the sum of all the solutions of the equation f(x)=0.6, 3≤x≤7. B denotes the fundamental period of g(x). C denotes the value of g′(6.75). Then, the value of [ABC] is (where [.] represents greatest integer function)
Answer» Let the function $f (x)$ and $g (x)$ be defined as $f (x) = ⎧ ⎨ ⎩ \begin{matrix} \sqrt{x} & 0 \leq x < 1 2 - x & 1 \leq x < 2 f (x + 2) & \forall x \in R \end{matrix}$ and $g (x) = 4 f (3 x) + 1, \forall x \in R$ . Let $A$ denotes the sum of all the solutions of the equation $f (x) = 0.6, 3 \leq x \leq 7$ . $B$ denotes the fundamental period of $g (x)$ . $C$ denotes the value of $g^{'} (6.75)$ . Then, the value of $[A B C]$ is (where [.] represents greatest integer function)