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Let f be continuous real-valued function with domain (a,6). Show that if =0 for each rational number r in (a,6) , then f(z) = 0 for all x â‚¬ (a,6). (b) Let f a...

Question

Let f be continuous real-valued function with domain (a,6). Show that if =0 for each rational number r in (a,6) , then f(z) = 0 for all x â‚¬ (a,6). (b) Let f and g be continuous real-valued functions on (a,b) such that f(r) = g(r) for each rational number in (a,6). Prove f() = g() for all & â‚¬ (a,6).

Let f be continuous real-valued function with domain (a,6). Show that if =0 for each rational number r in (a,6) , then f(z) = 0 for all x â‚¬ (a,6). (b) Let f and g be continuous real-valued functions on (a,b) such that f(r) = g(r) for each rational number in (a,6). Prove f() = g() for all & â‚¬ (a,6).

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