Functional equation in two variable part 2

Algebra Level 4

Find the value of f ( 99 ) f(99) , if we have f ( x ) + f ( x y ) = ( f ( x ) ) y + f ( y ) f(x) +f(xy) = \big(f(x)\big)^y+f(y) .

This problem is original.


The answer is 1.

Shivamani Patil by shivamani patil , 21, India

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2 solutions

Shivamani Patil
Aug 24, 2014

Now let y = 0 y=0 .

Then we have f ( x ) = 1 f(x)=1 .

And therefore for all values of x we have f ( x ) = 1 f(x)=1 .

So our answer is 1 1 .

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Answer is intuitive from the equation since there is one exponential expression and 3 linear.

Ankit Chabarwal - 6 years, 6 months ago
Fox To-ong
Jan 5, 2015

f(0)^99 + f(99) ^0= 1

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