If f : R → R is a function satisfying f ( x + y ) = f ( x y ) for all x , y ∈ R and f ( 4 3 ) = ( 4 3 ) , then f ( 16 9 ) =

Question

If f : R → R is a function satisfying f ( x + y ) = f ( x y ) for all x , y ∈ R and f ( 4 3 ​ ) = ( 4 3 ​ ) , then f ( 16 9 ​ ) =

TestHub · Accepted Answer

Let f ( 0 ) = k , then f ( x ) = f ( x + 0 ) = f ( 0 ) = k , f is a constant function. But f ( 4 3 ​ ) = ( 4 3 ​ ) ∴ f ( x ) = ( 4 3 ​ ) for all x and hence f ( 16 9 ​ ) = ( 4 3 ​ )

Mathematics - Functions Question with Solution | TestHub

Options:

Doubts & Discussion