Question

5. If f: R → R is a function with properties f(x + y) = f(x).f(y) for all x,y e R and f(1) = 3 then find the value of f(4).
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Answer 1

Answer :

f(4) = 81

Solution :

• Given :- f : R → R , f(x+y) = f(x)•f(y) , f(1) = 3

• To find :- f(4) = ?

We have ;

f(x + y) = f(x)•f(y) which is only possible when f(x) is an exponential function .

Thus ,

Let f(x) = a^x

Also ,

=> f(1) = 3

=> a^1 = 3

=> a = 3

Now ,

=> f(4) = a^4

=> f(4) = 3^4

=> f(4) = 81

Hence f(4) = 81 .