4. Let C[0, 1] be the inner product space with the inner product defined by (f,x)...

 

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4. Let C[0, 1] be the inner product space with the inner product defined by (f,x) = f' f(t)g(t)}dt. Consider the functions f(t) = 1+2t, g(t) = e¹, h(t) = cos 2лt. a. Compute the lengths of the functions f(t), g(t), and h(t). b. Compute the inner products (f,g), (f, h), (g, h). 4. Let C[0, 1] be the inner product space with the inner product defined by (f,x) = f' f(t)g(t)}dt. Consider the functions f(t) = 1+2t, g(t) = e¹, h(t) = cos 2лt. a. Compute the lengths of the functions f(t), g(t), and h(t). b. Compute the inner products (f,g), (f, h), (g, h).