Question 29814
Let f(x) = 9-x^2, g(x) = 3-x. Find (f+g) (x).
f(x) = 9-x^2   ----(1)
g(x) = 3-x.    ----(2)
(1) and (2) being polynomials in x are defined for all x
Now (f+g)(x)= f(x)+g(x)
= (9-x^2)+ (3-x)
=-x^2-x+12 (by additive commutativity and associativity)
which is again a polynomial in x defined for all x