Correct Answer - Option 3 : 6

__Concept__**:**

If g: A → B and f: B → C are functions then g o f (x) = g( f (x))

__Calculation:__

Given: f(x) = 3x and g(x) = log3 x

Here, we have to find the value of g o f(2) + g o f(4).

First lets find out the value of g o f(2)

⇒ g o f(2) = g( f(2))

∵ f(x) = 3x so, f(2) = 3^{2}

⇒ g o f(2) = g(3^{2})

∵ g(x) = log3 x so, g(32) = log_{3} (3^{2}) = 2

⇒ g o f(2) = 2 -------(1)

Similarly, lets find out the value of g o f(4)

g o f(4) = g( f(4))

∵ f(x) = 3x so, f(4) = 3^{4}

⇒ g o f(4) = g(3^{4})

∵ g(x) = log3 x so, g(3^{4}) = log3 (3^{4}) = 4

⇒ g o f(4) = 4 -------(2)

Now, from (1) and (2) we get,

⇒ g o f(2) + g o f(4) = 2 + 4 = 6