The gram–schmidt process for constructing an orthogonal set that was discussed in section 7.7 carries over to a linearly independent set { f0(x), f1(x), f2(x), …} of real-valued functions continuous on an interval [a, b]. with the inner product ( fn, fn) eb a fn(x)fn(x) dx, define the functions in the set b9 5f0(x), f1(x), f2(x), p 6 to be f0(x) f0(x) f1(x) f1(x) 2 ( f1, f0) (f0, f0) f0(x) f2(x) f2(x) 2 ( f2, f0) (f0, f0) f0(x) 2 ( f2, f1) (f1, f1) f1(x) o o and so on. (a) write out f3(x) in the set. (b) by construction, the set b9 5f0(x), f1(x), f2(x), p 6 is orthogonal on [a, b]. demonstrate that f0(x), f1(x), and f2(x) are mutually orthogonal.