For f(x) = 3x + 1 and g(x) = x2 – 6, find (f + g)(x)
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Check attached file for solution.
Not necessarily. 
and 
may be linearly dependent, so that their span forms a subspace of 
that does not contain every vector in .
For example, we could have
and 
. Any vector 
of the form 
, where 
, is impossible to obtain as a linear combination of these and , since
unless
and 
.
For example, we could have
unless