Consider the following functions. f1(x) = x, f,(x) = x², f,(x) = 3x – 7x2 g(x) = c,f;(x) + czf2(x) + C3f3(x) %3D Solve for c,, C2, and c, so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial...

Extracted text: Consider the following functions. f1(x) = x, f,(x) = x², f,(x) = 3x – 7x2 g(x) = c,f;(x) + czf2(x) + C3f3(x) %3D Solve for c,, C2, and c, so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {Cq, C2, C3} = { Determine whether f,, f,, fz are linearly independent on the interval (-0, o). 1' O linearly dependent linearly independent Need Help? Read It