Question 2. functions f : [0, 1] → R. Define an integral norm || · ||i by Let C[0, 1] represent the collection of continuous |f(x)| dx. We then introduce a distance function p which is given in terms of the integral norm || - ||i as P(f,9) := || f – 9|li Vf, g € C[0, 1] To show that < C0, 1], p > is a metric space: (a) Prove that the distance function p positive definite on C[0, 1]. (b) Is the distance function p is symmetric? Justify. (c) Show that p satisfies the triangle inequality on C[0, 1].

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A: The given proof is correct.

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A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

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A: According to our guidelines I can answer only Question no. 4(a).

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