f3(x) = 1/2(f1(x) - f2(x)) so we know that f3(x) is linearly dependent on f1,f2.Let S be the vector space consisting of the set of all linear combinations of the functions

f1(x)= e^(x)

f2(x)= e^(-x)

f3(x)= sinh(x)

Determine a basis for S, and hence, find dim[S].

Now, we consider f1(x),f2(x)

c1*f1(x) + c2*f2(x) = 0

c1 = c2 = 0. f1 and f2 are Linearly independent and are a basis. Dim[S] = 2.

Is my answer correct?

Thanks