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) = 32
⇒ g o f(2) = g(32)
∵ g(x) = log3 x so, g(32) = log3 (32) = 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) = 34
⇒ g o f(4) = g(34)
∵ g(x) = log3 x so, g(34) = log3 (34) = 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