11. [-/7.5 Points]
DETAILS
Consider the following functions.
$f_1(x) = e^x$, $f_2(x) = e^{-x}$, $f_3(x) = \sinh(x)$
$g(x) = c_1f_1(x) + c_2f_2(x) + c_3f_3(x)$
Solve for $c_1$, $c_2$, and $c_3$ so that $g(x) = 0$ on the interval $(-\infty, \infty)$. If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution $(0, 0, 0)$.)
$\{c_1, c_2, c_3\} = \{
\}$
Determine whether $f_1, f_2, f_3$ are linearly independent on the interval $(-\infty, \infty)$.
$\circ$ linearly dependent
$\circ$ linearly independent
