Question

Let F denote the set of real-valued continuous functions on [0, 1]. If f, g ∈ F, define
f + g and fg by
• (f + g)(x) = f(x) + g(x) for all x ∈ [0, 1], and
• (fg)(x) = f(x)g(x) for all x ∈ [0, 1].
Is F a field with these two binary operations?

Answer 1

Answer:

f=(0,1) ,g=(0,1)

f+g= (0,1)

(fg)= (0,1),(1,0),(0,0),(1,1)

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