How many times Continuous

Calculus Level 2

Find the number of continuous functions f satisfying

x f ( y ) + y f ( x ) = ( x + y ) f ( x ) × f ( y ) x f(y) + yf(x) = (x+y) f(x) \times f(y)

where x and y are any real numbers.

4 2 3 1

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2 solutions

Mayank Holmes
May 20, 2014

put y=1 and x=1 ........... simplifying the obtained equation , you will get f(1) = 0,1 ......... hence it is pretty clear that there are two different values for one input ... hence two different mappings!

Bryan Dellariarte
Mar 12, 2014

:p

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