Determine whether the given function is linear or nonlinear. If the function is nonlinear, explain why. [Hint:Recall that a linear function is of the form f (x1; : : : ; xn) = c1x1 + + cnxn where c1; : : : ; cn are constants.](a) f (x; y) = x + 2y(b) g(x1; x2; x3) = cos(x1 + x2 + x3)(c) h(x1; x2; x3; x4) = 6x1 45 x2 + 178 x3 x4(d) k(x1; : : : ; xn) = 3(x1 + + xn 1)(e) f (x1; x2) = x21 x1x2

Question

Determine whether the given function is linear or nonlinear. If the function is nonlinear, explain why. [Hint:

Recall that a linear function is of the form f (x1; : : : ; xn) = c1x1 + + cnxn where c1; : : : ; cn are constants.]

(a) f (x; y) = x + 2y

(b) g(x1; x2; x3) = cos(x1 + x2 + x3)

(c) h(x1; x2; x3; x4) = 6x1 45 x2 + 178 x3 x4

(d) k(x1; : : : ; xn) = 3(x1 + + xn 1)

(e) f (x1; x2) = x21 x1x2

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