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
Thank you for the question, since we are entitled to answer up to 3 sub-parts, we’ll answer the first 3 as you have not mentioned the sub-parts you need help with. Please resubmit the question and specify the other sub-parts you’d like to get answered.
Since, a linear function is of the form as shown follows:
For sub-part (a)
We determine its linearity as follows:
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