Question

"48. If a function satisfies\n\\[ \\begin{aligned} & ( x - y ) f ( x + y ) - ( x + y ) f ( x - y ) \\\\ = & 2 \\left( x ^ { 2 } y - y ^ { 3 } \\right) , \\forall x , y \\in R \\text { and } f ( 1 ) = 2 , \\text { then } \\\\ \\text { (a) } f ( x ) \\text { must be polynomial function } \\\\ \\text { (b) } f ( 3 ) = 12 \\\\ \\text { (c) } f ( 0 ) = 12 \\\\ \\text { (d) } f ( x ) \\text { may not be differentiable } \\end{aligned} \\]"

Answer 1