Consider the following functions. f,(x) = 2 + x, f,(x) = x, f;(x) = x² g(x) = cf,(x) + cf2(x) + czf3(x) Solve for c,, Ca, and c, so that g(x) = 0 on the interval (-, o). If a nontrivial solution...

Extracted text: Consider the following functions. f,(x) = 2 + x, f,(x) = x, f;(x) = x² g(x) = cf,(x) + cf2(x) + czf3(x) Solve for c,, Ca, and c, so that g(x) = 0 on the interval (-, o). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution (0, 0, 0}.) {c,, c2, c3} = Determine whether f,, fa, f, are linearly independent on the interval (-, ). o linearly dependent linearly independent