take each of the options and check whether it satisfies the given properties of f

eg option (a) f(x,y) = m+ xy

replace x by x and y by y+k ie f(x, y + k) = m+x(y+k)= m+xy+kx=f(x,y)+kx : satisfies.

note that it also satisfies remaining 2 properties (given)

option b and c doesn't satisfy

hence option a

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"You don't have to believe in God, but you should believe in The Book." -Paul Erdős