Additional exercise (5 points): Given a vector w E S and a real number t, we denote by Pw,t the plane Pw,t = {x E R3 : (w, x) = t}. Let f : R3 - C be a smooth function that vanishes outside a bounded set. The Radon transform of f is defined by ( Rf ) (w, t ) = Jp. . for all w E S2 and t E R. Note that Rf is a function from S2 x R to C. Let F : $2 x R - C be a smooth function that vanishes outside a bounded set. The the dual Radon transform of F is defined by (R* F) (2) = F(w, ( w, 20) ) dw for all x E R3. Note that R*F is a function from R3 to C. Please show that ( Rf ) ( w , t ) F ( w , t ) at ) dw = / f ( 2 ) ( R * F ) (x ) dac . $2 OO