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See the answer Find ∂z/∂x and ∂z/∂y (a. C F ár =!. Is a function g from the reals to the reals, whose domain is the set of the reals x, such that f(x) ≠ 0 The range of a function is the set of the images of all elements in the domain However, range is sometimes used as a synonym of codomain, generally in old textbooks citation neededRelational approach Any subset of the Cartesian product of two sets and defines a binary relation.

X' Y Z X (b) ((X’Y’)’(X’Z’)’)’ X' Y' X' Z' X Y X Z 24 (Gate Logic) Draw the schematics for the following functions using NAND gates and inverters only (a) (X(Y’Z’))’ = X Z' Y' X Z' Y' X Z Y (b) XY XZ = X X Y Z X X Y Z X Y Z X 25 (Gate Logic) Design a hall light circuit to the following specification There is a. 2y, 2z> S x = u,y = v,z =5 !. A B y t p ¬ 8.

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4 Let f R → R by f(x) = 2x2 1 and g R → R by g(x) = 3x−10 Find g f and f g f g(x) = f(g(x)) = f(3x−10) = 2(3x−10)2 1 g f(x) = g(f(x)) = g(2x2 1) = 3(2x2 1)−10 5 Prove whether each of the following functions is onetoone or not and whether it is onto its codomain or not (a) f R → R by f(x) = 12x3 5 • ONETO.