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If f(x) = 3x and g(x) = log3 x then find the value of g o f(2) + g o f(4) ?
1. 2
2. 4
3. 6
4. 1
5. None of these

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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

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